A character formula for a family of simple modular representations of GL(n)

Citation
O. Mathieu et G. Papadopoulo, A character formula for a family of simple modular representations of GL(n), COMM MATH H, 74(2), 1999, pp. 280-296
Citations number
24
Categorie Soggetti
Mathematics
Journal title
COMMENTARII MATHEMATICI HELVETICI
ISSN journal
00102571 → ACNP
Volume
74
Issue
2
Year of publication
1999
Pages
280 - 296
Database
ISI
SICI code
0010-2571(1999)74:2<280:ACFFAF>2.0.ZU;2-C
Abstract
Let K be an algebraically closed field of finite characteristic p, and let n greater than or equal to 1 be an integer. In the paper, we give a charact er formula for all simple rational representations of GL,(K) with highest w eight any multiple of any fundamental weight. Our formula. is slightly more general: say that a dominant weight lambda is special if there are integer s i less than or equal to j such that lambda = Sigma(i less than or equal t o k less than or equal to j) a(k)w(k) and Sigma(i less than or equal to k l ess than or equal to j) a(k) less than or equal to inf(p - (j - i),p - 1). Indeed, we compute the character of any simple module whose highest weight lambda can be written as lambda = lambda(0) + p lambda(1) +...+ p(r)lambda( r) with all Xi are special. By stabilization, we get a character formula fo r a family of irreducible rational GL(infinity)(K)-modules.