Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel
Let $M$ be the tensor product of finite-dimensional polynomial evaluation Yangian $Y(gl_N)$-modules. Consider the universal difference operator $D = sum_{k=0}^N (-1)^k T_k(u) e^{-kpartial_u}$ whose coefficients $T_k(u): M o M$ are the XXX transfer matrices associated with $M$. We show that the diffe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-04-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/060/ |
| _version_ | 1819054601467330560 |
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| author | Evgeny Mukhin Vitaly Tarasov Alexander Varchenko |
| author_facet | Evgeny Mukhin Vitaly Tarasov Alexander Varchenko |
| author_sort | Evgeny Mukhin |
| collection | DOAJ |
| description | Let $M$ be the tensor product of finite-dimensional polynomial evaluation Yangian $Y(gl_N)$-modules. Consider the universal difference operator $D = sum_{k=0}^N (-1)^k T_k(u) e^{-kpartial_u}$ whose coefficients $T_k(u): M o M$ are the XXX transfer matrices associated with $M$. We show that the difference equation $Df = 0$ for an $M$-valued function $f$ has a basis of solutions consisting of quasi-exponentials. We prove the same for the universal differential operator $D = sum_{k=0}^N (-1)^k S_k(u) partial_u^{N-k}$ whose coefficients $S_k(u) : M o M$ are the Gaudin transfer matrices associated with the tensor product $M$ of finite-dimensional polynomial evaluation $gl_N[x]$-modules. |
| first_indexed | 2024-12-21T12:54:13Z |
| format | Article |
| id | doaj.art-e2ef6ef3b5de42c7a1e820c77e720b20 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-21T12:54:13Z |
| publishDate | 2007-04-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-e2ef6ef3b5de42c7a1e820c77e720b202022-12-21T19:03:24ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-04-013060Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential KernelEvgeny MukhinVitaly TarasovAlexander VarchenkoLet $M$ be the tensor product of finite-dimensional polynomial evaluation Yangian $Y(gl_N)$-modules. Consider the universal difference operator $D = sum_{k=0}^N (-1)^k T_k(u) e^{-kpartial_u}$ whose coefficients $T_k(u): M o M$ are the XXX transfer matrices associated with $M$. We show that the difference equation $Df = 0$ for an $M$-valued function $f$ has a basis of solutions consisting of quasi-exponentials. We prove the same for the universal differential operator $D = sum_{k=0}^N (-1)^k S_k(u) partial_u^{N-k}$ whose coefficients $S_k(u) : M o M$ are the Gaudin transfer matrices associated with the tensor product $M$ of finite-dimensional polynomial evaluation $gl_N[x]$-modules.http://www.emis.de/journals/SIGMA/2007/060/Gaudin modelXXX modeluniversal differential operator |
| spellingShingle | Evgeny Mukhin Vitaly Tarasov Alexander Varchenko Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel Symmetry, Integrability and Geometry: Methods and Applications Gaudin model XXX model universal differential operator |
| title | Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel |
| title_full | Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel |
| title_fullStr | Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel |
| title_full_unstemmed | Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel |
| title_short | Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel |
| title_sort | generating operator of xxx or gaudin transfer matrices has quasi exponential kernel |
| topic | Gaudin model XXX model universal differential operator |
| url | http://www.emis.de/journals/SIGMA/2007/060/ |
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