Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm

David Hernandez, Hironori Oya

研究成果: Article

1 引用 (Scopus)

抜粋

We establish ring isomorphisms between quantum Grothendieck rings of certain remarkable monoidal categories C Q,B n and C Q,A 2n−1 of finite-dimensional representations of quantum affine algebras of types B n (1) and A 2n−1 (1) , respectively. Our proof relies in part on the corresponding quantum cluster algebra structures. Moreover, we prove that our isomorphisms specialize at t=1 to the isomorphisms of (classical) Grothendieck rings obtained recently by Kashiwara, Kim and Oh by other methods. As a consequence, we prove a conjecture formulated by the first author in 2002: the multiplicities of simple modules in standard modules in C Q,B n are given by the specialization of certain analogues of Kazhdan-Lusztig polynomials and the coefficients of these polynomials are positive.

元の言語English
ページ(範囲)192-272
ページ数81
ジャーナルAdvances in Mathematics
347
DOI
出版物ステータスPublished - 2019 4 30

    フィンガープリント

ASJC Scopus subject areas

  • Mathematics(all)

これを引用