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International Mathematics Research Notices (2003) 2003:2193-2203 , doi:10.1155/S107379280313022X
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Copyright © 2003 Hindawi Publishing Corporation. All rights reserved.

On the Poincaré series of quadratic algebras associated to Hecke symmetries

Nguy{ecirctilde}n Phuong Dung and Phùng H{ocircgrave} Hai

Hecke symmetries generalize the usual tensor symmetry of vector spaces Formula as well as the symmetry of vector superspaces. To a Hecke symmetry there associates a quadratic algebra which can be interpreted as the function algebra upon a certain quantum space. This paper investigates the Poincaré series of this quadratic algebra. We show that it is a rational function with numerator and denominator being a reciprocal polynomial and a skew-reciprocal polynomial, respectively.


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