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- W1768642008 abstract "We compute $E_G (prod_i tr(g^{lambda_i}))$, where $G=Sp(2n)$ or $SO(m) (m=2n, 2n+1)$ with Haar measure. This was first obtained by Persi Diaconis and Mehrdad Shahshahani, but our proof is more self-contained and gives a combinatorial description for the answer. We also consider how averages of general symmetric functions $E_G f_n$ are affected when we introduce a Weyl character $chi^G_lambda$ into the integrand. We show that the value of $E_G chi^G_lambda f_n / E_G f_n$ approaches a constant for large $n$. More surprisingly, the ratio we obtain only changes with $f_n$ and $lambda$ and is independent of the Cartan type of $G$. Even in the unitary case, Daniel Bump and Persi Diaconis have obtained the same ratio. Finally, those ratios can be combined with asymptotics for $E_G f_n$ due to Kurt Johansson and provide asymptotics for $E_G chi^G_lambda f_n$." @default.
- W1768642008 created "2016-06-24" @default.
- W1768642008 creator A5063283785 @default.
- W1768642008 date "2005-04-20" @default.
- W1768642008 modified "2023-09-27" @default.
- W1768642008 title "Averages over classical compact Lie groups and Weyl characters" @default.
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