Hall algebras of cyclic quivers and q-deformed Fock spaces

JOURNAL OF ALGEBRA

卷:480

Article

Deng, Bangming¹  Xiao, Jie² 

[1] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

关键词: Cyclic quiver;    Ringel-Hall algebra;    Quantum group;    Fock space;   

DOI  :  10.1016/j.jalgebra.2017.02.006

来源: Elsevier

【 摘 要 】

Based on the work of Riegel and Green, one can define the (Drinfeld) double Ringel-Hall algebra D(Q) of a quiver Q as well as its highest weight modules. The main purpose of the present paper is to show that the basic representation L(Lambda(0)) of D(Delta(n)) of the cyclic quiver An, provides a realization of the q-deformed Fock space A defined by Hayashi. This is worked out by extending a construction of Varagnolo and Vasserot. By analysing the structure of nilpotent representations of An we obtain a decomposition of the basic representation L(Lambda(0)) which induces the Kashiwara-Miwa-Stern decomposition of Lambda(infinity)) and a construction of the canonical basis of A defined by Leclerc and Thibon in terms of certain monomial basis elements in D(Delta(n)). (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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