2015/09/16 by Daniele Rosso, Rosso, Daniele
Mathematics · #17B10 (Secondary) #17B37 (Primary) #20G43 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.QA #math.RA #math.RT #msc:17B10 #msc:17B37 #msc:20G43
paper · pdf · doi:10.48550/arxiv.1509.04790
34 pages
arxiv created 2015/09/16 · openalex publication_date 2015/09/16 · arxiv updated 2015/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The quantum enveloping algebra of \mathfraksln (and the quantum Schur algebras) was constructed by Beilinson-Lusztig-MacPherson as the convolution algebra of GLd-invariant functions over the space of pairs of partial n-step flags over a finite field. In this paper we expand the construction to the mirabolic setting of triples of two partial flags and a vector, and examine the resulting convolution algebra. In the case of n=2, we classify the finite dimensional irreducible representations of the mirabolic quantum algebra and we prove that the category of such representations is semisimple. Finally, we describe a mirabolic version of the quantum Schur-Weyl duality, which involves the mirabolic Hecke algebra.