On Chari-Loktev bases for local Weyl modules in type A

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:154

Article

Raghavan, K. N.¹  Ravinder, B.²  Viswanath, Sankaran¹ 

[1] HBNI, Inst Math Sci, CIT Campus, Madras 600113, Tamil Nadu, India

[2] Tata Inst Fundamental Res, Homi Bhabha Rd, Bombay 400005, Maharashtra, India

关键词: Gelfand-Tsetlin pattern;    Chari-Loktev basis;    Demazure module;    Partition overlaid pattern POP;    Area of a pattern;    Stability of Chari-Loktev bases;   

DOI  :  10.1016/j.jcta.2017.08.011

来源: Elsevier

【 摘 要 】

This paper is a study of the bases introduced by Chari-Loktev in [1] for local Weyl modules of the current algebra associated to a special linear Lie algebra. Partition overlaid patterns, POPs for short-whose introduction is one of the aims of this paper-form convenient parametrizing sets of these bases. They play a role analogous to that played by (Gelfand-Ibetlin) patterns in the representation theory of the special linear Lie algebra. The notion of a POP leads naturally to the notion of area of a pattern. We observe that there is a unique pattern of maximal area among all those with a given bounding sequence and given weight. We give a combinatorial proof of this and discuss its representation theoretic relevance. We then state a conjecture about the stability, i.e., compatibility in the long range, of Chari-Loktev bases with respect to inclusions of local Weyl modules. In order to state the conjecture, we establish a certain bijection between colored partitions and POPs, which may be of interest in itself. The stability conjecture has been proved in [6] in the rank one case. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free