Quantum affine algebras and affine Hecke algebras
نویسندگان
چکیده
منابع مشابه
QUANTUM AFFINE gln VIA HECKE ALGEBRAS
The quantum loop algebra of gln is the affine analogue of quantum gln. In the seminal work [1], Beilinson–Lusztig–MacPherson gave a beautiful realisation for quantum gln via a geometric setting of quantum Schur algebras. Since then, generalising this work to the affine case and other cases (see, e.g., [9]) attracted much attention. For example, in [13, 21, 15, 20], affine quantum Schur algebras...
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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...
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The Hecke group algebra H W̊ of a finite Coxeter group W̊ , as introduced by the first and last author, is obtained from W̊ by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when W̊ is the classical Weyl group associated to an affine Weyl group W . Namely, we prove that, for q not a root of unity, H W̊ is the ...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1996
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1996.174.295