Fundamental Representations of Quantum Affine Superalgebras and R-Matrices

Zhang, Huafeng

doi:10.1007/s00031-016-9405-6

Cited by 13 publications

(9 citation statements)

References 16 publications

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“…The R-matrices that appear in the Yang-Baxter equations are (up to Drinfeld twisting) known as "Perk-Schultz" or supersymmetric R-matrices with an already-substantial literature [42,4,52,51,34]. However the RTT Yang-Baxter equations presented in Section 2.4 are new and different from other known Yang-Baxter equations that involve the R-matrix alone.…”

Section: Iwahori Vector Whittaker Functionalmentioning

confidence: 99%

Metaplectic Iwahori Whittaker functions and supersymmetric lattice models

Brubaker¹,

Buciumas²,

Bump³

et al. 2020

Preprint

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In this paper we consider Iwahori Whittaker functions on n-fold metaplectic covers G of G(F ) with G a split reductive group over a non-archimedean local field F . For every element φ of a basis of Iwahori Whittaker functions, and for every g ∈ G, we evaluate φ(g) by recurrence relations over the Weyl group using "vector Demazure-Whittaker operators." Specializing to the case of G = GL r , we exhibit a solvable lattice model whose partition function equals φ(g). These models are of a new type associated with the quantum affine super group U q ( gl(r|n)). The recurrence relations on the representation theory side then correspond to solutions to Yang-Baxter equations for the lattice models.

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Section: Iwahori Vector Whittaker Functionalmentioning

confidence: 99%

Metaplectic Iwahori Whittaker functions and supersymmetric lattice models

Brubaker¹,

Buciumas²,

Bump³

et al. 2020

Preprint

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“…cit. can be simplified and strengthened by Weyl modules, as indicated in the proof of [8, Theorem 2.6(iii)]; see a closer situation in[34, Proposition 5.2].…”

mentioning

confidence: 99%

Baxter operators and asymptotic representations

Felder¹,

Zhang²

2017

Sel. Math. New Ser.

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Abstract. We introduce a category O of representations of the elliptic quantum group associated with sl 2 with well-behaved q-character theory. We derive separation of variables relations for asymptotic representations in the Grothendieck ring of this category. Baxter Q-operators are obtained as transfer matrices for asymptotic representations and obey T Q-relations as a consequence of the relations in K 0 (O).

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“…There are other recent works on the finite-dimensional representations of quantum affine superalgebra associated to gl M|N [24,25,26]. It would be interesting to compare with these results.…”

Section: Introductionmentioning

confidence: 90%

$R$ matrix for generalized quantum group of type $A$

Kwon

2020

Preprint

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The generalized quantum group U (ǫ) of type A is an affine analogue of quantum group associated to a general linear Lie superalgebra gl M |N . We prove that there exists a unique R matrix on tensor product of fundamental type representations of U (ǫ) for arbitrary parameter sequence ǫ corresponding to a non-conjugate Borel subalgebra of gl M |N . We give an explicit description of its spectral decomposition, and then as an application, construct a family of finite-dimensional irreducible U (ǫ)-modules which have subspaces isomorphic to the Kirillov-Reshetikhin modules of usual affine type A

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Fundamental Representations of Quantum Affine Superalgebras and R-Matrices

Cited by 13 publications

References 16 publications

Metaplectic Iwahori Whittaker functions and supersymmetric lattice models

Metaplectic Iwahori Whittaker functions and supersymmetric lattice models

Baxter operators and asymptotic representations

$R$ matrix for generalized quantum group of type $A$

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