有限一般线性群与酉群的实character度和的Generating functions
Generating functions for real character degree sums of finite general linear and unitary groups
摘要：
通过对称函数的计算，我们计算了有限一般线性群和酉群的实值特征标度之和的生成函数。对于有限一般线性群，给出了实值特征标具有Frobenius-Schur指标1的一个新的组合证明，并得到了一些q-级数恒等式.对于有限酉群，将生成函数用Hall-Littlewood函数的值展开，得到了Frobenius-Schur指标为1或-1的实值特征标的特征标度和的组合表达式.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
