On Multiplicative Invariants of Finite Reflection Groups |
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Authors: | Mohammed Tesemma |
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Institution: | 1. Department of Mathematics , Spelman College , Atlanta, Georgia, USA mtesemma@spelman.edu |
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Abstract: | This article focuses on two recent results on multiplicative invariants of finite reflection groups: Lorenz (2001
Lorenz , M. ( 2001 ). Multiplicative invariants and semigroup algebras . Alg. and Rep. Theory 4 : 293 – 304 . Google Scholar]) showed that such invariants are affine normal semigroup algebras, and Reichstein (2003
Reichstein , Z. ( 2003 ). SAGBI bases in rings of multiplicative invariants . Commentarii Math. Helvetici 78 ( 1 ): 185 – 202 .Web of Science ®] , Google Scholar]) proved that the invariants have a finite SAGBI basis. Reichstein (2003
Reichstein , Z. ( 2003 ). SAGBI bases in rings of multiplicative invariants . Commentarii Math. Helvetici 78 ( 1 ): 185 – 202 .Web of Science ®] , Google Scholar]) also showed that, conversely, if the multiplicative invariant algebra of a finite group G has a SAGBI basis, then G acts as a reflection group. There is no obvious connection between these two results. We will show that multiplicative invariants of finite reflection groups have a certain embedding property that implies both results simultaneously. |
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Keywords: | Monomial order Multiplicative action Reflection group SAGBI basis Semigroup algebra |
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