00 5 The Ŵ - orbit of ρ , Kostant ’ s formula for powers of the Euler product and affine Weyl groups as permutations of Z Paola Cellini Pierluigi
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چکیده
Let an affine Weyl group Ŵ act as a group of affine transformations on a real vector space V . We analyze the Ŵ -orbit of a regular element in V and deduce applications to Kostant’s formula for powers of the Euler product and to the representations of Ŵ as permutations of the integers.
منابع مشابه
2 00 6 The Ŵ - orbit of ρ , Kostant ’ s formula for powers of the Euler product and affine Weyl groups as permutations of Z Paola
Let an affine Weyl group Ŵ act as a group of affine transformations on a real vector space V . We analyze the Ŵ -orbit of a regular element in V and deduce applications to Kostant’s formula for powers of the Euler product and to the representations of Ŵ as permutations of the integers.
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متن کاملPowers of the Euler product and commutative subalgebras of a complex simple Lie algebra
If g is a complex simple Lie algebra, and k does not exceed the dual Coxeter number of g, then the k coefficient of the dim g power of the Euler product may be given by the dimension of a subspace of ∧g defined by all abelian subalgebras of g of dimension k. This has implications for all the coefficients of all the powers of the Euler product. Involved in the main results are Dale Peterson’s 2 ...
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تاریخ انتشار 2005