Geodesic
Generating functions for real character degree sums of finite general linear and unitary groups
Journal of Algebraic Combinatorics, Tome 40 (2014) no. 2, pp. 387-416.

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

We compute generating functions for the sum of the real-valued character degrees of the finite general linear and unitary groups, through symmetric function computations. For the finite general linear group, we get a new combinatorial proof that every real-valued character has Frobenius-Schur indicator 1, and we obtain some $q$-series identities. For the finite unitary group, we expand the generating function in terms of values of Hall-Littlewood functions, and we obtain combinatorial expressions for the character degree sums of real-valued characters with Frobenius-Schur indicator 1 or $-1$.
Classification : 05E15, 05E05, 05A15
Keywords: Frobenius-Schur indicator, real-valued characters, involutions, finite general linear group, finite unitary group, generating functions, $q$-series, Hall-Littlewood polynomial 
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     title = {Generating functions for real character degree sums of finite general linear and unitary groups},
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Fulman, Jason; Vinroot, C.Ryan. Generating functions for real character degree sums of finite general linear and unitary groups. Journal of Algebraic Combinatorics, Tome 40 (2014) no. 2, pp. 387-416. http://geodesic.mathdoc.fr/item/JAC_2014__40_2_a7/