R matrix for generalized quantum group of type A

JOURNAL OF ALGEBRA

卷:566

Article

Kwon, Jae-Hoon^1,2  Yu, Jeongwoo¹ 

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

关键词: Quantum group;    Crystal base;    Lie superalgebra;    R matrix;   

DOI  :  10.1016/j.jalgebra.2020.09.009

来源: Elsevier

【 摘 要 】

The generalized quantum group U(epsilon) of type A is an affine analogue of quantum group associated to a general linear Lie superalgebra gl(M vertical bar N). We prove that there exists a unique R matrix on the tensor product of fundamental type representations of U(epsilon) for arbitrary parameter sequence E corresponding to a non-conjugate Borel subalgebra of gl(M vertical bar N). We give an explicit description of its spectral decomposition, and then as an application, construct a family of finite-dimensional irreducible U(epsilon)-modules which have subspaces isomorphic to the Kirillov-Reshetikhin modules of usual affine type A(M -)( 1)(()(1)) or A(N - )(1)((1)). (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free