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triangular group

Proceedings of the Edinburgh Mathematical Society (1)

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Supercharacters and pattern subgroups in the upper triangular groups
Part of
- Representation theory of groups
Tung Le
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 1 / February 2013

Published online by Cambridge University Press:

21 November 2012, pp. 177-186
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Let Un(q) denote the upper triangular group of degree n over the finite field with q elements. It is known that irreducible constituents of supercharacters partition the set of all irreducible characters Irr(Un(q)). In this paper we present a correspondence between supercharacters and pattern subgroups of the form Uk(q) ∩ wUk(q), where w is a monomial matrix in GLk(q) for some k < n.