Geodesic
Unipotent Brauer character values of ${GL} (n,\bbfF_q)$ and the forgotton basis of the Hall algebra
Journal of Algebraic Combinatorics, Tome 13 (2001) no. 2, pp. 137-149.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We give a formula for the values of irreducible unipotent $p$-modular Brauer characters of $GL( n, \mathbb F _{ q} ) GL(n, \mathbb{F}_q )$ at unipotent elements, where $p$ is a prime not dividing $q$, in terms of (unknown!) weight multiplicities of quantum $GL _{ n }$ and certain generic polynomials $S \_$ lambda, mgr( q). These polynomials arise as entries of the transition matrix between the renormalized Hall-Littlewood symmetric functions and the forgotten symmetric functions. We also provide an alternative combinatorial algorithm working in the Hall algebra for computing S _ lambda, mgr( q).
Keywords: symmetric function, general linear group, unipotent representation, Brauer character 
@article{JAC_2001__13_2_a5,
     author = {Brundan, Jonathan},
     title = {Unipotent {Brauer} character values of ${GL} (n,\bbfF_q)$ and the forgotton basis of the {Hall} algebra},
     journal = {Journal of Algebraic Combinatorics},
     pages = {137--149},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2001__13_2_a5/}
}
TY  - JOUR
AU  - Brundan, Jonathan
TI  - Unipotent Brauer character values of ${GL} (n,\bbfF_q)$ and the forgotton basis of the Hall algebra
JO  - Journal of Algebraic Combinatorics
PY  - 2001
SP  - 137
EP  - 149
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2001__13_2_a5/
LA  - en
ID  - JAC_2001__13_2_a5
ER  - 
%0 Journal Article
%A Brundan, Jonathan
%T Unipotent Brauer character values of ${GL} (n,\bbfF_q)$ and the forgotton basis of the Hall algebra
%J Journal of Algebraic Combinatorics
%D 2001
%P 137-149
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2001__13_2_a5/
%G en
%F JAC_2001__13_2_a5
Brundan, Jonathan. Unipotent Brauer character values of ${GL} (n,\bbfF_q)$ and the forgotton basis of the Hall algebra. Journal of Algebraic Combinatorics, Tome 13 (2001) no. 2, pp. 137-149. http://geodesic.mathdoc.fr/item/JAC_2001__13_2_a5/