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arXiv · 1306.0031

Generating functions for real character degree sums of finite general linear and unitary groups

Jason Fulman·C. Ryan Vinroot
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Abstract

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.

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Jason Fulman, C. Ryan Vinroot. 2013-05-31. Generating functions for real character degree sums of finite general linear and unitary groups. https://arxiv.org/abs/1306.0031

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