The paper contains an exposition of two contributions of Mackey, together with a more recent result of Kawanaka and Matsuyama, generalized by Bump and Ginzburg, on the representation theory of a finite group equipped with an involutory anti-automorphism. Mackey’s first contribution is a detailed version of the so-called Gelfand criterion for weakly symmetric Gelfand pairs. Mackey’s second contribution is a characterization of simply reducible groups (a notion introduced by Wigner). The other result is a twisted version of the Frobenius-Schur theorem, where “twisted” refers to the above-mentioned involutory anti-automorphism.
The paper contains an exposition of two contributions of Mackey, together with a more recent result of Kawanaka and Matsuyama, generalized by Bump and Ginzburg, on the representation theory of a finite group equipped with an involutory anti-automorphism. Mackey’s first contribution is a detailed version of the so-called Gelfand criterion for weakly symmetric Gelfand pairs. Mackey’s second contribution is a characterization of simply reducible groups (a notion introduced by Wigner). The other result is a twisted version of the Frobenius-Schur theorem, where “twisted” refers to the above-mentioned involutory anti-automorphism.
Mackey's theory of tau-conjugate representations for finite groups / Scarabotti, Fabio; Tullio, Ceccherini Silberstein; Filippo, Tolli. - In: JAPANESE JOURNAL OF MATHEMATICS. NEW SERIES. - ISSN 0289-2316. - STAMPA. - 10:1(2015), pp. 43-96. [10.1007/s11537-014-1390-8]
Mackey's theory of tau-conjugate representations for finite groups
SCARABOTTI, Fabio;
2015
Abstract
The paper contains an exposition of two contributions of Mackey, together with a more recent result of Kawanaka and Matsuyama, generalized by Bump and Ginzburg, on the representation theory of a finite group equipped with an involutory anti-automorphism. Mackey’s first contribution is a detailed version of the so-called Gelfand criterion for weakly symmetric Gelfand pairs. Mackey’s second contribution is a characterization of simply reducible groups (a notion introduced by Wigner). The other result is a twisted version of the Frobenius-Schur theorem, where “twisted” refers to the above-mentioned involutory anti-automorphism.| File | Dimensione | Formato | |
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Note: Mackey tau conjugate
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