Affiliation:
1. Department of Mathematics , Indian Institute of Science Education and Research , Pune - 411008, Maharashtra , India
Abstract
Abstract
We describe the Stiefel–Whitney classes (SWCs) of orthogonal representations 𝜋 of the finite special linear groups
G
=
SL
(
2
,
F
q
)
G=\operatorname{SL}(2,\mathbb{F}_{q})
, in terms of character values of 𝜋.
From this calculation, we can answer interesting questions about SWCs of 𝜋.
For instance, we determine the subalgebra of
H
*
(
G
,
Z
/
2
Z
)
H^{*}(G,\mathbb{Z}/2\mathbb{Z})
generated by the SWCs of orthogonal 𝜋, and we also determine which 𝜋 have non-trivial mod 2 Euler class.
Subject
Algebra and Number Theory
Reference23 articles.
1. A. Adem and R. J. Milgram,
Cohomology of Finite Groups,
Grundlehren Math. Wiss. 309,
Springer, Berlin, 2004.
2. D. J. Benson,
Representations and Cohomology. II: Cohomology of Groups and Modules,
Cambridge Stud. Adv. Math. 31,
Cambridge University, Cambridge, 1998.
3. T. Bröcker and T. tom Dieck,
Representations of Compact Lie Groups,
Grad. Texts in Math. 98,
Springer, New York, 1995.
4. D. Bump,
Automorphic Forms and Representations,
Cambridge Stud. Adv. Math. 55,
Cambridge University, Cambridge, 1998.
5. C. J. Bushnell and G. Henniart,
The Local Langlands Conjecture for
GL
(
2
)
\mathrm{GL}(2)
,
Grundlehren Math. Wiss. 335,
Springer, Berlin, 2006.