Bases of the quantum matrix bialgebra and induced sign characters of the\n Hecke algebra

2018/02/13 by Ryan Kaliszewski, Kaliszewski, Ryan, Justin Lambright +3 · 2 citations
Mathematics · #(Primary) 20C08 #05A05 #05A15 (Secondary) #05E10 #16T20 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1802.04856

openalex publication_date 2018/02/13 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We combinatorially describe entries of the transition matrices which relate\nmonomial bases of the zero-weight space of the quantum matrix bialgebra. This\ndescription leads to a combinatorial rule for evaluating induced sign\ncharacters of the type A Hecke algebra H_n(q) at all elements of the form\n(1 + T_s_i1) \⋯ (1 + T_s_im), including the Kazhdan-Lusztig\nbasis elements indexed by 321-hexagon-avoiding permutations. This result is\nthe first subtraction-free rule for evaluating all elements of a basis of the\nH_n(q)-trace space at all elements of a basis of H_n(q).\n

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• Factorizations in Hecke algebras I: long cycle factorizations and Jucys-Murphy elements
• A generalization of Deodhar's defect statistic for Iwahori--Hecke algebras of type BC

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