Integral Solutions to Schlesinger Equations
It is shown that Schlesinger equations for isomonodromic deformations of Fuchsian systems of order p on the Riemann spheres with upper triangular monodromy are reduced to multidimensional linear homogeneous ( p = 2) and inhomogeneous (≥ 3) Pfaffian systems. For components of the solutions to the mul...
Saved in:
| Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 208; no. 2; pp. 229 - 239 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
02.07.2015
Springer |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | It is shown that Schlesinger equations for isomonodromic deformations of Fuchsian systems of order
p
on the Riemann spheres with upper triangular monodromy are reduced to multidimensional linear homogeneous (
p
= 2) and inhomogeneous (≥ 3) Pfaffian systems. For components of the solutions to the multidimensional linear Pfaffian systems (
p
= 2) we obtain integral representations of hypergeometric type and expressions in quadratures close to the hypergeometric Schlesinger equations describing deformations of upper triangular Fuchsian systems of order
p
= 3. |
|---|---|
| AbstractList | It is shown that Schlesinger equations for isomonodromic deformations of Fuchsian systems of order
p
on the Riemann spheres with upper triangular monodromy are reduced to multidimensional linear homogeneous (
p
= 2) and inhomogeneous (≥ 3) Pfaffian systems. For components of the solutions to the multidimensional linear Pfaffian systems (
p
= 2) we obtain integral representations of hypergeometric type and expressions in quadratures close to the hypergeometric Schlesinger equations describing deformations of upper triangular Fuchsian systems of order
p
= 3. It is shown that Schlesinger equations for isomonodromic deformations of Fuchsian systems of order p on the Riemann spheres with upper triangular monodromy are reduced to multidimensional linear homogeneous (p = 2) and inhomogeneous ([greater than or equal to] 3) Pfaffian systems. For components of the solutions to the multidimensional linear Pfaffian systems (p = 2) we obtain integral representations of hypergeometric type and expressions in quadratures close to the hypergeometric Schlesinger equations describing deformations of upper triangular Fuchsian systems of order p = 3. Bibliography: 11 titles. |
| Audience | Academic |
| Author | Leksin, V. P. |
| Author_xml | – sequence: 1 givenname: V. P. surname: Leksin fullname: Leksin, V. P. email: lexin_vp@mail.ru organization: Moscow State Region Institute of Social Studies and Humanities |
| BookMark | eNp9kUFLwzAUx4MouE0_gLeBJ5HMJC9p0uMYUwcDwek5xDSpHV2rSQv67c2sl8GQHBLyfr8H7_3H6LRpG4fQFSUzSoi8i5TkQmFCBWacEwwnaESFBKxkLk7Tm0iGASQ_R-MYtyQ5mYIRul01nSuDqaebtu67qm3itGunG_teu1g1pQvT5WdvfgsX6MybOrrLv3uCXu-XL4tHvH56WC3ma2w5ZYC5zBxQpnghmVA5kIwayZjPvBeZKXJlCvBOOWGNMqlkPQECbwYkyT0YAxN0PfQtTe101fi2C8buqmj1nIsMeGorE4WPUKVrXJomLcdX6fuAnx3h0yncrrJHhZsDITGd--pK08eoV5vnQ5YOrA1tjMF5_RGqnQnfmhK9D0gPAekUkN4HpCE5bHBiYveb1tu2D03a7D_SDwhikSk |
| CitedBy_id | crossref_primary_10_1080_14029251_2017_1375692 |
| Cites_doi | 10.1134/S0081543812060132 10.1023/A:1020763318762 10.1090/cbms/098 10.1090/conm/078/975088 10.4153/CMB-2001-006-3 10.1016/0167-2789(81)90013-0 10.1515/crll.1905.129.287 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media New York 2015 COPYRIGHT 2015 Springer |
| Copyright_xml | – notice: Springer Science+Business Media New York 2015 – notice: COPYRIGHT 2015 Springer |
| DBID | AAYXX CITATION ISR |
| DOI | 10.1007/s10958-015-2440-3 |
| DatabaseName | CrossRef Gale In Context: Science |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1573-8795 |
| EndPage | 239 |
| ExternalDocumentID | A456342587 10_1007_s10958_015_2440_3 |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C -~X .86 .VR 06D 0R~ 0VY 1N0 1SB 2.D 29L 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 642 67Z 6NX 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AABYN AAFGU AAHNG AAIAL AAJKR AANZL AARHV AARTL AATNV AATVU AAUYE AAWCG AAYFA AAYIU AAYQN AAYTO ABBBX ABBXA ABDBF ABDZT ABECU ABFGW ABFTV ABHLI ABHQN ABJNI ABJOX ABKAS ABKCH ABKTR ABMNI ABMQK ABNWP ABPTK ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACBMV ACBRV ACBXY ACBYP ACGFS ACHSB ACHXU ACIGE ACIPQ ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACSNA ACTTH ACVWB ACWMK ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADMDM ADOXG ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEEQQ AEFIE AEFTE AEGAL AEGNC AEJHL AEJRE AEKMD AEOHA AEPOP AEPYU AESKC AESTI AETLH AEVLU AEVTX AEXYK AFEXP AFFNX AFGCZ AFLOW AFMKY AFNRJ AFQWF AFWTZ AFZKB AGAYW AGDGC AGGBP AGGDS AGJBK AGMZJ AGPAZ AGQMX AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIIXL AILAN AIMYW AITGF AJBLW AJDOV AJRNO AKQUC ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AZFZN B-. B0M BA0 BAPOH BBWZM BDATZ BGNMA CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP EAD EAP EAS EBLON EBS EIOEI EJD EMK EPL ESBYG ESX FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS HF~ HG6 HMJXF HQYDN HRMNR HVGLF HZ~ IAO IEA IHE IJ- IKXTQ IOF ISR ITC IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C JBSCW JCJTX JZLTJ KDC KOV KOW LAK LLZTM M4Y MA- N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P9R PF0 PT4 PT5 QOK QOS R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC TUS U2A UG4 UNUBA UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 XU3 YLTOR Z7R Z7U Z7X Z7Z Z81 Z83 Z86 Z88 Z8M Z8R Z8T Z8W Z92 ZMTXR ZWQNP ~8M ~A9 ~EX AACDK AAEOY AAJBT AASML AAYXX ABAKF ACAOD ACDTI ACZOJ AEARS AEFQL AEMSY AFBBN AGQEE AGRTI AIGIU CITATION H13 AAYZH |
| ID | FETCH-LOGICAL-c4123-476e31284d725893061a722f6ff56ad98ad3fe8e5ca8a1a7cf0303ba3709f3aa3 |
| IEDL.DBID | AGYKE |
| ISSN | 1072-3374 |
| IngestDate | Thu Feb 22 23:55:37 EST 2024 Fri Feb 02 05:08:55 EST 2024 Tue Nov 12 22:48:00 EST 2024 Thu Aug 01 20:03:38 EDT 2024 Thu Sep 12 20:01:29 EDT 2024 Sat Dec 16 12:07:56 EST 2023 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Fundamental Matrix Monodromy Matrix Holomorphic Vector Bundle Riemann Sphere Vector Bundle |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c4123-476e31284d725893061a722f6ff56ad98ad3fe8e5ca8a1a7cf0303ba3709f3aa3 |
| PageCount | 11 |
| ParticipantIDs | gale_infotracmisc_A456342587 gale_infotracgeneralonefile_A456342587 gale_infotracacademiconefile_A456342587 gale_incontextgauss_ISR_A456342587 crossref_primary_10_1007_s10958_015_2440_3 springer_journals_10_1007_s10958_015_2440_3 |
| PublicationCentury | 2000 |
| PublicationDate | 20150702 |
| PublicationDateYYYYMMDD | 2015-07-02 |
| PublicationDate_xml | – month: 07 year: 2015 text: 20150702 day: 02 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Journal of mathematical sciences (New York, N.Y.) |
| PublicationTitleAbbrev | J Math Sci |
| PublicationYear | 2015 |
| Publisher | Springer US Springer |
| Publisher_xml | – name: Springer US – name: Springer |
| References | BolibrukhAAInverse Monodromy Problems in Analytic Theory of Differential Equations [in Russian]2009MoscowMTcNMO A. Varchenko, Special Functions, KZ Type Equations, and Representation Theory, Am. Math. Soc., Providence, RI (2003). JimboMMiwaTUenoKMonodromy preserving deformations of linear differential equations with rational coefficients. I. General theory and τ -functionPhysica D198123063521194.3416763067410.1016/0167-2789(81)90013-0 MalekS“Fuchsian systems with reducible monodromy are meromorphically equivalent to reducible Fuchsian systems”, [in Russian]Tr. Mat. Inst. Steklova20022364814901931047 MalekSOn the reducibility of the Schlesinger equationsJ. Dyn. Contr. Syst.2002845055271020.34086193189610.1023/A:1020763318762 V. P. Leksin, “Multidimensional Jordan–Pochhammer systems and their applications” [in Russian], Tr. Mat. Inst. Steklova278, 138–147 (2012); English transl.: 278, 130–138 (2012). I. V. Vyugin and R. R. Gontsov, “On the question of solvability of Fuchsian systems by quadratures” [in Russian], Usp. Mat. Nauk67, No. 3, 183–184 (2012); English transl.Russ. Math. Surv.67, No. 3, 585–587 (2012). SchlesingerLÜber die Lösungen gewisser linearer Differentialgleichungen als Funktionen der singulären PunkteJ. Reine Angew. Math.19051292872941580670 KohnoTLinear representations of braid groups and classical Yang–Baxter equationsContemp. Math.198878339363975088 KapovichMMillsonJQuantization of bending deformations of polygons in E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbb{E} $$\end{document}3, hypergeometric integrals and the Gassner representationCanad. Math. Bull.20014436601008.53073181604810.4153/CMB-2001-006-3 MalgrangeBSur les déformations isomonodromiques. I. Singularités régulièresProgr. Math.198337401426728431 2440_CR11 T Kohno (2440_CR9) 1988; 78 S Malek (2440_CR8) 2002; 8 AA Bolibrukh (2440_CR3) 2009 2440_CR1 M Jimbo (2440_CR5) 1981; 2 2440_CR7 S Malek (2440_CR6) 2002; 236 B Malgrange (2440_CR4) 1983; 37 M Kapovich (2440_CR10) 2001; 44 L Schlesinger (2440_CR2) 1905; 129 |
| References_xml | – ident: 2440_CR1 doi: 10.1134/S0081543812060132 – volume: 8 start-page: 505 issue: 4 year: 2002 ident: 2440_CR8 publication-title: J. Dyn. Contr. Syst. doi: 10.1023/A:1020763318762 contributor: fullname: S Malek – ident: 2440_CR11 doi: 10.1090/cbms/098 – volume: 78 start-page: 339 year: 1988 ident: 2440_CR9 publication-title: Contemp. Math. doi: 10.1090/conm/078/975088 contributor: fullname: T Kohno – ident: 2440_CR7 – volume-title: Inverse Monodromy Problems in Analytic Theory of Differential Equations [in Russian] year: 2009 ident: 2440_CR3 contributor: fullname: AA Bolibrukh – volume: 236 start-page: 481 year: 2002 ident: 2440_CR6 publication-title: Tr. Mat. Inst. Steklova contributor: fullname: S Malek – volume: 44 start-page: 36 year: 2001 ident: 2440_CR10 publication-title: Canad. Math. Bull. doi: 10.4153/CMB-2001-006-3 contributor: fullname: M Kapovich – volume: 37 start-page: 401 year: 1983 ident: 2440_CR4 publication-title: Progr. Math. contributor: fullname: B Malgrange – volume: 2 start-page: 306 year: 1981 ident: 2440_CR5 publication-title: Physica D doi: 10.1016/0167-2789(81)90013-0 contributor: fullname: M Jimbo – volume: 129 start-page: 287 year: 1905 ident: 2440_CR2 publication-title: J. Reine Angew. Math. doi: 10.1515/crll.1905.129.287 contributor: fullname: L Schlesinger |
| SSID | ssj0007683 |
| Score | 2.0394967 |
| Snippet | It is shown that Schlesinger equations for isomonodromic deformations of Fuchsian systems of order
p
on the Riemann spheres with upper triangular monodromy are... It is shown that Schlesinger equations for isomonodromic deformations of Fuchsian systems of order p on the Riemann spheres with upper triangular monodromy are... |
| SourceID | gale crossref springer |
| SourceType | Aggregation Database Publisher |
| StartPage | 229 |
| SubjectTerms | Mathematics Mathematics and Statistics |
| Title | Integral Solutions to Schlesinger Equations |
| URI | https://link.springer.com/article/10.1007/s10958-015-2440-3 |
| Volume | 208 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3JTsMwEB1BucCBHVGWKkIIJFCqYmc9BmjZVA6USnCyHMcuUlEKTXrh6xlngwg4cM4oicfjmadZngEOpVTU9rkwz1SHm5YbWWaIYddE5BqGQmrCdp2H7N8710Pr9sl-mgNSpS7icbusSGaO-tusm2_rvivbJLoeSedhoZg7XQiunu-6lf9FAJ231bvEpNS1ylrmby-pRaPSJ9crolmg6a3kw39Jxk-o-0vG7VkatsXHT_bGf6xhFZYL3GkEuaGswZyM12GpX5G2JhuQZQdHU5SqcmVGOjEG4uVVJtlnjO57zgyebMKw1328uDaLuxRMYaGScBccSXUsilxiI0bBMM5dQpSjlO3wyPd4RJX0pC24x_GRUHj6acip2_EV5ZxuQSOexHIbjFAJxCCevtmPWg6XHrd85XYi6kUc8Q5pwkmpU_aWU2awL3JkrQGGGmBaA4w24UBrnWkqilj3uoz4LEnYzeCBBYjtKLoUz23CcSGkJumUC16MDuD_aPaqmuRRTXKUc3f_JrhXE8RDJWqPT8sdZMWhTv5exM6_pHdhkWgT0DlisgeNdDqT-4hs0rCFpnx-ed5rFSbdgvkhCT4BfXDt9g |
| link.rule.ids | 315,783,787,27936,27937,41093,41535,42162,42604,52123,52246 |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LSwMxEA5aD-pBfGK16iKioARqsrvZPRaxtNr2YFvoLWSzST3IVrvt_3dmH9WFevCcj5BMHvMxM_lCyI0xlnuh0vTRNhV1RezSCNwuBeYaRdqgYDvGIfsDvzN2XybepHjHnZbV7mVKMrupfz12Cz0svPIow4Qk3yRbKK-Ogvlj1lpdv8Cf86p6wSjnwi1Tmeu6qDij8kquJkQzP9PeJ3sFQXRa-YoekA2THJLd_kpdNT0iWRhvOgfUKqjlLGbOUL9_mDTr1Hn-yiW802Mybj-Pnjq0-PSAahe8CJjLNxydRiyYB2QC_K0SjFnfWs9XcRiomFsTGE-rQEGTtnBMeaS4aIaWK8VPSC2ZJeaUOJHVQBYC_IKPu74ygXJDK5oxD2IFxITVyX05e_mZa1vIHxVjNJUEU0k0leR1co32kagZkWBRylQt01R2h2-yBSSMw9kPRJ3cFSA7W8yVVkWNP4wHZaYqyNsKcpqLbK8DNipA2P260vxQrpcsTl_69yTO_oW-ItudUb8ne93B6znZYbhvMLDLGqS2mC_NBdCRRXSZbb9vaFXSrg |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3fS8MwEA46QfRB_InTqUVEQSmbSdu0j0M3NnVDnIO9hWuazAfp5tr9_17WdlqYDz7nIySXH_dxd_lCyJVSmrkBSPteN8B2eOTYIbpdG5lrGEplBNtNHLLX9zpD52nkjvJ_TpOi2r1ISWZvGoxKU5zWp5Gu_3r4FrimCMu1qUlOsnWygZ6ImZq-IW0ur2Lk0lmFPac2Y9wp0pqruig5puJ6LidHFz6nvUt2crJoNbPV3SNrKt4n272l0mpyQBYhvfEMUcsAl5VOrIH8-FTJolOr9ZXJeSeHZNhuvT907PwDBFs66FHQdJ5ixoFEnLpILND3AqdUe1q7HkSBDxHTyleuBB-wSWo8siwExhuBZgDsiFTiSayOiRVqicTBN9_xMccD5YMTaN6ImB8BkhRaJbfF7MU007kQP4rGxlQCTSWMqQSrkktjH2H0I2JToDKGeZKI7uBNNJGQMbwHfF4lNzlIT9IZSMjr_XE8RnKqhLwuIceZ4PYqYK0ExJMgS813xXqJ_CQmf0_i5F_oC7L5-tgWL93-8ynZombbmBgvrZFKOpurM2QmaXi-2H3f_pHW8w |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Integral+solutions+to+Schlesinger+equations&rft.jtitle=Journal+of+mathematical+sciences+%28New+York%2C+N.Y.%29&rft.au=Leksin%2C+V.P&rft.date=2015-07-02&rft.pub=Springer&rft.issn=1072-3374&rft.eissn=1573-8795&rft.volume=208&rft.issue=2&rft.spage=229&rft_id=info:doi/10.1007%2Fs10958-015-2440-3&rft.externalDBID=ISR&rft.externalDocID=A456342587 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1072-3374&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1072-3374&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1072-3374&client=summon |