Spin Hecke Algebras of Finite and Affine Types
نویسنده
چکیده
We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine) Hecke-Clifford algebras of Olshanski and Jones-Nazarov. Relation between the spin (affine) Hecke algebra and a nonstandard presentation of the usual (affine) Hecke algebra is displayed, and the notion of covering (affine) Hecke algebra is introduced to provide a link between these algebras. Various algebraic structures for the spin (affine) Hecke algebra are established.
منابع مشابه
Double Affine Hecke Algebras for the Spin Symmetric Group
We introduce a new class (in two versions, Au and Bu) of rational double affine Hecke algebras (DaHa) associated to the spin symmetric group. We establish the basic properties of the algebras, such as PBW and Dunkl representation, and connections to Nazarov’s degenerate affine Hecke algebra and to a new degenerate affine Hecke algebra introduced here. We formulate a precise connection between t...
متن کاملAffine Hecke algebras, cyclotomic Hecke algebras and Clifford theory
We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, B and D, Iwahori-Hecke algebras of types A, B, and D, the complex reflection groups G(r, p, n) and the corresponding cyclotomic Hecke algebras Hr,p,n, can be obtained, in all cases, from the affine Hecke algebra of type A. The Young tableaux theory was extended to affine Hec...
متن کاملAffine braids , Markov traces and the category
This paper provides a unified approach to results on representations of affine Hecke algebras, cyclotomic Hecke algebras, affine BMW algebras, cyclotomic BMW algebras, Markov traces, Jacobi-Trudi type identities, dual pairs [Ze], and link invariants [Tu2]. The key observation in the genesis of this paper was that the technical tools used to obtain the results in Orellana [Or] and Suzuki [Su], t...
متن کامل2 1 A pr 1 99 8 LIE ALGEBRAS AND DEGENERATE AFFINE HECKE ALGEBRAS OF TYPE
We construct a family of exact functors from the BernsteinGelfand-Gelfand category O of sln-modules to the category of finite-dimensional representations of the degenerate affine Hecke algebra Hl of GLl. These functors transform Verma modules to standard modules or zero, and simple modules to simple modules or zero. Any simple Hl-module can be thus obtained. Introduction The classical Frobenius...
متن کاملA Family of Finite-Dimensional Representations of Generalized Double Affine Hecke Algebras of Higher Rank
We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for Uq(slN ). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld–Kohno theorem for Knizhnik–Zamolodchikov differential equations, we prove that the explicit representatio...
متن کامل