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Monoidal categories of modules over quantum affine algebras of type A and B
Author(s) -
Kashiwara Masaki,
Kim Myungho,
Oh Sejin
Publication year - 2019
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12160
Subject(s) - mathematics , quantum affine algebra , bijection , isomorphism (crystallography) , ring (chemistry) , functor , pure mathematics , quiver , type (biology) , derived category , subcategory , affine transformation , grothendieck group , noetherian ring , simple module , closed monoidal category , discrete mathematics , simple (philosophy) , algebra over a field , enriched category , cellular algebra , finitely generated abelian group , algebra representation , philosophy , ecology , chemistry , crystal structure , biology , abelian group , epistemology , organic chemistry , crystallography
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 C B n ( 1 )of finite‐dimensional integrable modules over the quantum affine algebra of type B n ( 1 ) . It factors through the category T 2 n , which is a localization of A . As a result, this functor induces a ring isomorphism from the Grothendieck ring of T 2 n(ignoring the gradings) to the Grothendieck ring of a subcategory C B n ( 1 ) 0 of C B n ( 1 ). Moreover, it induces a bijection between the classes of simple objects. Because the category T 2 nis related to categories C A 2 n − 1 ( t ) 0( t = 1 , 2 ) of the quantum affine algebras of type A 2 n − 1 ( t ) , 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 C A 2 n − 1 ( t ) 0 and the Grothendieck ring of C B n ( 1 ) 0 , which induces a bijection between the classes of simple modules.