Dual canonical bases, quantum shuffles and q-characters

2002/09/11 by Bernard Leclerc, Leclerc, Bernard · 2 citations
Mathematics · #17B37 #20C08 #20G42 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37 #msc:20C08 #msc:20G42

paper · pdf · doi:10.48550/arxiv.math/0209133

36 pages, final version, to appear in Math. Zeitschrift

openalex publication_date 2002/09/11 · arxiv created 2003/06/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Rosso and Green have shown how to embed the positive part U_q(n) of a quantum enveloping algebra U_q(g) in a quantum shuffle algebra. In this paper we study some properties of the image of the dual canonical basis B^* of U_q(n) under this embedding Φ. This is motivated by the fact that when g is of type A_r, the elements of Φ(B^*) are q-analogues of irreducible characters of the affine Iwahori-Hecke algebras attached to the groups GL(m) over a p-adic field.

Cited by

• Freidel-Maillet type equations on fused K-matrices over the positive part of U_q(\widehat\mathfraksl₂)
• Categorification of quantum boson algebras

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