2016/06/03 by K. N. Raghavan, Raghavan, K. N., B. Ravinder +3 · 2 citations
Mathematics · #05E10 #17B67 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1606.01191
openalex publication_date 2016/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is a study of the bases introduced by Chari-Loktev 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-Tsetlin) 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.