### Bitraces for gln(fq) and the iwahori-hecke algebra of type an-1 (1999).Bitraces for gln(fq) and the iwahori-hecke algebra of type an-1 (1999).

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 Author Halverson, Tom ♦ Ram, Awn Source CiteSeerX Content type Text File Format PDF
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract Let H,,(q) be the Iwahori-Hecke algebra of the symmetric group S,,. Let F, be a finite field with y elements and let B be the Bore1 subgroup of upper triangular matrices in the general linear group G = GL,(F,). Let 1: denote the trivial representation of B induced to G. Then H,,(q) has a natural action on 1; that commutes with the G-action, and we define the bitrace btr(g, a) to be the trace of g E G and a E H,(q) acting simultaneously in lg. For partitions, p, v of n, let Tw be a standard basis element of H,,(q) corresponding to the S,-conjugacy class p, and let u, be a unipotent element of G with Jordan block structure V. We give a combinatorial formula for btr(u,, Tp) as a weighted sum of column strict tableaux of shape v and content p. This bitrace also essentially counts Ifs-rational points in the intersection of a conjugacy class with a Schubert cell, provides a new proof of the Frobenius formula for characters of H,(q), and gives a natural pairing between the conjugacy classes of S, and the unipotent classes in G. Educational Role Student ♦ Teacher Age Range above 22 year Educational Use Research Education Level UG and PG ♦ Career/Technical Study Publisher Date 1999-01-01