Monoidal categories of modules over quantum affine algebras of type A and B
- 주제(키워드) 16G99 , 16T25 , 17B37 (primary) , 81R50
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted
- 발행기관 John Wiley and Sons Ltd.
- 발행년도 2019
- URI http://www.dcollection.net/handler/ewha/000000156820
- 본문언어 영어
- Published As http://dx.doi.org/10.1112/plms.12160
초록/요약
We construct an exact tensor functor from the category A of finite-dimensional graded modules over the quiver Hecke algebra of type A∞ to the category CBn(1) of finite-dimensional integrable modules over the quantum affine algebra of type Bn 1. It factors through the category T2n, which is a localization of A. As a result, this functor induces a ring isomorphism from the Grothendieck ring of T2n (ignoring the gradings) to the Grothendieck ring of a subcategory C0 Bn(1) of CBn(1). Moreover, it induces a bijection between the classes of simple objects. Because the category T2n is related to categories (Formula presented.) (t = 1, 2) of the quantum affine algebras of type A(1) 2n-1, we obtain an interesting connection between those categories of modules over quantum affine algebras of type A and type B. Namely, for each t = 1, 2, there exists an isomorphism between the Grothendieck ring of C0 Bn(1) and the Grothendieck ring of (Formula presented.), which induces a bijection between the classes of simple modules. © 2018 London Mathematical Society
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