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.
2015
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.
Representation theory of finite groups; Gelfand pair; Kronecker product; Simply reducible group; Clifford groups; Frobenius-Schur theorem
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/645806
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