DUALITIES AND DIMENSIONS OF IRREDUCIBLE REPRESENTATIONS OF PARABOLIC SUBGROUPS OF LOW DEGREES

Nguyen Dang Ho Hai and Ton That Tri

Abstract

          Let GL_{n1, ..., nr} be a parabolic subgroup of the general linear group GL_n over the prime field F_p of p elements. A complete set of distinct irreducible modules for Fp[GL_{n1, ..., nr}] was explicitly constructed in [7]. In this paper, we use this construction to determine the contragredient dual module of each  Fp[GL_n1,...,nr]-irreducible module and prove that its dimension can be computed via the dimensions of some  Fp[GL_ni]-irreducible modules.