On modular invariants of a vector and a covector |
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Authors: | Yin Chen |
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Affiliation: | 1. School of Mathematics and Statistics, Northeast Normal University, 5268 Remin Street, Changchun, 130024, People’s Republic of China 2. Chern Institute of Mathematics, Nankai University, Tianjin, 300071, People’s Republic of China
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Abstract: | Let GL 2(F q ) be the general linear group over a finite field F q , V be the 2-dimensional natural representation of GL 2(F q ) and V * be the dual representation. We denote by ({F_{q}[Voplus V^{ast}]^{GL_{2}(F_{q})}}) the corresponding invariant ring of a vector and a covector for GL 2(F q ). In this paper, we prove that ({F_{q}[Voplus V^{ast}]^{GL_{2}(F_{q})}}) is a Gorenstein algebra. This result confirms a special case (n = 2) of the recent conjecture of Bonnafé and Kemper (J Algebra 335:96–112, 2011). |
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