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...
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doaj-f56d03c2125a40989d0f76a56ddf716d2020-11-24T22:23:47ZengElsevierNuclear 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 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zengo Tsuboi |
spellingShingle |
Zengo Tsuboi Asymptotic representations and q-oscillator solutions of the graded Yang–Baxter equation related to Baxter Q-operators Nuclear Physics B |
author_facet |
Zengo Tsuboi |
author_sort |
Zengo Tsuboi |
title |
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_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_sort |
asymptotic representations and q-oscillator solutions of the graded yang–baxter equation related to baxter q-operators |
publisher |
Elsevier |
series |
Nuclear Physics B |
issn |
0550-3213 1873-1562 |
publishDate |
2014-09-01 |
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]. |
url |
http://www.sciencedirect.com/science/article/pii/S0550321314002004 |
work_keys_str_mv |
AT zengotsuboi asymptoticrepresentationsandqoscillatorsolutionsofthegradedyangbaxterequationrelatedtobaxterqoperators |
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1725763970117140480 |