Tokyo Journal of Mathematics

On the Centralizer Algebras of the Primitive Unitary Reflection Group of Order 96

Masashi KOSUDA and Manabu OURA

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Abstract

Among the unitary reflection groups, the one on the title is singled out by its importance in, for example, coding theory and number theory. In this paper we examine the semi-simple structure of the centralizer algebra in the tensor representation, and show that the dimensions of the centralizers coincide with the numbers of some combinatorial objects.

Article information

Source
Tokyo J. Math., Volume 39, Number 2 (2016), 469-482.

Dates
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1484903133

Digital Object Identifier
doi:10.3836/tjm/1484903133

Mathematical Reviews number (MathSciNet)
MR3599504

Zentralblatt MATH identifier
1358.05306

Subjects
Primary: 05E10: Combinatorial aspects of representation theory [See also 20C30]
Secondary: 05E05: Symmetric functions and generalizations 05E15: Combinatorial aspects of groups and algebras [See also 14Nxx, 22E45, 33C80] 05A18: Partitions of sets

Citation

KOSUDA, Masashi; OURA, Manabu. On the Centralizer Algebras of the Primitive Unitary Reflection Group of Order 96. Tokyo J. Math. 39 (2016), no. 2, 469--482. doi:10.3836/tjm/1484903133. https://projecteuclid.org/euclid.tjm/1484903133


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