Coinvariant Theory of a Coxeter Group

Howard L. Hiller
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Howard L. Hiller: Oxford University, Mathematical Institute

A chapter in The Geometric Vein, 1981, pp 555-559 from Springer

Abstract: Abstract Let G be a finite group represented on a real vector space V. We can make G act on the polynomial algebra S(V) on V by g · f(x) = f(g −1 x). Classical invariant theory studies the invariant subalgebra $$ S{\left( V \right)^G}\;{\rm{ = }}\mathop \oplus \limits_{j = 0}^\infty \;{S_j}{\left( V \right)^G}. $$ Alternatively, one has the graded, homogeneous ideal I G , generated by the positive components of S(V) G , and we can form the quotient algebra S G = S(V)/I G . For convenience, we call this the coinvariant algebra of G and its elements coinvariants (though this terminology has been used for other purposes).

Keywords: Weyl Group; Coxeter Group; Polynomial Algebra; Algebra Cohomology; Schubert Cell (search for similar items in EconPapers)
Date: 1981
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DOI: 10.1007/978-1-4612-5648-9_37

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