B-Orbits in solutions to the equation X2 = 0 in triangular matrices

Anna Melnikov

doi:10.1006/jabr.1999.8056

B-Orbits in solutions to the equation X² = 0 in triangular matrices

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Abstract

Consider I_n(K), the set of solutions to the equation X²=0 in n×n strictly upper-triangular matrices over field K. In this paper we construct the bijection from the set of adjoint orbits in I_n(K) onto the set of involutions in symmetric group S_n. For a finite field K we compute the number of points in the orbits.

Original language	English
Pages (from-to)	101-108
Number of pages	8
Journal	Journal of Algebra
Volume	223
Issue number	1
DOIs	https://doi.org/10.1006/jabr.1999.8056
State	Published - 1 Jan 2000
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jabr.1999.8056

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abstract = "Consider In(K), the set of solutions to the equation X2=0 in n×n strictly upper-triangular matrices over field K. In this paper we construct the bijection from the set of adjoint orbits in In(K) onto the set of involutions in symmetric group Sn. For a finite field K we compute the number of points in the orbits.",

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B-Orbits in solutions to the equation X² = 0 in triangular matrices

Abstract

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