Modified Affine Hecke Algebras and Drinfeldians of Type A

Details Modified Affine Hecke Algebras and Drinfeldians of Type A Modified Affine Hecke Algebras and Drinfeldians of Type A

1999-12-08

arxiv.org/abs/math/9912063v1

Mathematics

Quantum Algebra

11 pages, LATEX. Contribution to Proceedings "Quantum Theory and Symmetries" (Goslar, July 18-22, 1999) (World Scientific, 200

Scientific paper

We introduce a modified affine Hecke algebra $\h{H}^{+}_{q\eta}({l})$ ($\h{H}_{q\eta}({l})$) which depends on two deformation parameters $q$ and $\eta$. When the parameter $\eta$ is equal to zero the algebra $\h{H}_{q\eta=0}(l)$ coincides with the usual affine Hecke algebra $\h{H}_{q}(l)$ of type $A_{l-1}$, if the parameter q goes to 1 the algebra $\h{H}^{+}_{q=1\eta}(l)$ is isomorphic to the degenerate affine Hecke algebra $\Lm_{\eta}(l)$ introduced by Drinfeld. We construct a functor from a category of representations of $H_{q\eta}^{+}(l)$ into a category of representations of Drinfeldian $D_{q\eta}(sl(n+1))$ which has been introduced by the first author.

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