JP Journal of Algebra, Number Theory and Applications
Volume 41, Issue 1, Pages 59 - 83
(January 2019) http://dx.doi.org/10.17654/NT041010059 |
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LIFTINGS OF PSEUDO-REFLECTION GROUPS OF TORIC QUOTIENTS OF KRULL SCHEMES
Haruhisa Nakajima
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Abstract: Let G be an affine algebraic group with a reductive identity component G0 acting regularly on an affine Krull scheme X = Spec(R) over an algebraically closed field. Let T be an algebraic subtorus of G and suppose that of quotient fields. We will show: If G is the centralizer of T in G, then the pseudo-reflections of the action of G on RT can be lifted to those on R. This result is applied to partially generalize Chevalley-Serre and Steinberg theorems on pseudo-reflection groups. |
Keywords and phrases: algebraic torus, pseudo-reflection, Krull domain, ramification index, invariant theory.
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