Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators
We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra Uq(glˆ(M|N)). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of Uq(gl(M|N)) in the FRT formulation and obtain explicit solutions of the graded Y...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2014-09-01
|
| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321314002004 |
| _version_ | 1819259284396965888 |
|---|---|
| author | Zengo Tsuboi |
| author_facet | Zengo Tsuboi |
| author_sort | Zengo Tsuboi |
| collection | DOAJ |
| description | We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra Uq(glˆ(M|N)). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of Uq(gl(M|N)) in the FRT formulation and obtain explicit solutions of the graded Yang–Baxter equation in terms of q-oscillator superalgebras. These solutions correspond to L-operators for Baxter Q-operators. We also discuss an extension of these representations to the ones for contracted algebras of Uq(glˆ(M|N)) by considering the action of renormalized generators of the other side of the Borel subalgebra. We define model independent universal Q-operators as the supertrace of the universal R-matrix and write universal T-operators in terms of these Q-operators based on shift operators on the supercharacters. These include our previous work on Uq(slˆ(2|1)) case [1] in part, and also give a cue for the operator realization of our Wronskian-like formulas on T- and Q-functions in [2,3]. |
| first_indexed | 2024-12-23T19:07:34Z |
| format | Article |
| id | doaj.art-f56d03c2125a40989d0f76a56ddf716d |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-12-23T19:07:34Z |
| publishDate | 2014-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-f56d03c2125a40989d0f76a56ddf716d2022-12-21T17:34:33ZengElsevierNuclear Physics B0550-32131873-15622014-09-01886C13010.1016/j.nuclphysb.2014.06.017Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operatorsZengo TsuboiWe consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra Uq(glˆ(M|N)). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of Uq(gl(M|N)) in the FRT formulation and obtain explicit solutions of the graded Yang–Baxter equation in terms of q-oscillator superalgebras. These solutions correspond to L-operators for Baxter Q-operators. We also discuss an extension of these representations to the ones for contracted algebras of Uq(glˆ(M|N)) by considering the action of renormalized generators of the other side of the Borel subalgebra. We define model independent universal Q-operators as the supertrace of the universal R-matrix and write universal T-operators in terms of these Q-operators based on shift operators on the supercharacters. These include our previous work on Uq(slˆ(2|1)) case [1] in part, and also give a cue for the operator realization of our Wronskian-like formulas on T- and Q-functions in [2,3].http://www.sciencedirect.com/science/article/pii/S0550321314002004 |
| spellingShingle | Zengo Tsuboi Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators Nuclear Physics B |
| title | Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators |
| title_full | Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators |
| title_fullStr | Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators |
| title_full_unstemmed | Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators |
| title_short | Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators |
| title_sort | asymptotic representations and q oscillator solutions of the graded yang baxter equation related to baxter q operators |
| url | http://www.sciencedirect.com/science/article/pii/S0550321314002004 |
| work_keys_str_mv | AT zengotsuboi asymptoticrepresentationsandqoscillatorsolutionsofthegradedyangbaxterequationrelatedtobaxterqoperators |