On the dimensions of cartesian symmetry classes

Yousef Zamani; Mohammad Shahryari

doi:10.1142/S1793557112500465

On the dimensions of cartesian symmetry classes

Yousef Zamani^*, Mohammad Shahryari

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

The notion of Cartesian symmetry classes is introduced in [T. G. Lei, Notes on Cartesian symmetry classes and generalized trace functions, Linear Algebra Appl. 292 (1999) 281[288]. In this paper, we discuss these classes and compute the dimensions of these classes in terms of the fixed point character of S _m. Also, we give a formula for the dimension of Cartesian symmetry class V ^χ(G) in terms of the rank of an idempotent matrix M(χ). Some properties of generalized trace functions of a matrix are concluded.

Original language	English
Article number	1250046
Journal	Asian-European Journal of Mathematics
Volume	5
Issue number	3
DOIs	https://doi.org/10.1142/S1793557112500465
Publication status	Published - Sept 2012
Externally published	Yes

Keywords

Cartesian symmetry classes
Irreducible characters
generalized trace functions

ASJC Scopus subject areas

Mathematics(all)

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10.1142/S1793557112500465

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AB - The notion of Cartesian symmetry classes is introduced in [T. G. Lei, Notes on Cartesian symmetry classes and generalized trace functions, Linear Algebra Appl. 292 (1999) 281[288]. In this paper, we discuss these classes and compute the dimensions of these classes in terms of the fixed point character of S m. Also, we give a formula for the dimension of Cartesian symmetry class V χ(G) in terms of the rank of an idempotent matrix M(χ). Some properties of generalized trace functions of a matrix are concluded.

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KW - Irreducible characters

KW - generalized trace functions

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On the dimensions of cartesian symmetry classes

Abstract

Keywords

ASJC Scopus subject areas

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