Representations of affine quantum function algebras
نویسندگان
چکیده
منابع مشابه
Quantum Z-algebras and Representations of Quantum Affine Algebras
Generalizing our earlier work, we introduce the homogeneous quantum Z-algebras for all quantum affine algebras Uq(ĝ) of type one. With the new algebras we unite previously scattered realizations of quantum affine algebras in various cases. As a result we find a realization of Uq(F (1) 4 ). 0. Introduction In 1981 Lepowsky and Wilson introduced (principal) Z-algebras as a tool to construct expli...
متن کاملVertex representations of quantum affine algebras.
We construct vertex representations of quantum affine algebras of ADE type, which were first introduced in greater generality by Drinfeld and Jimbo. The limiting special case of our construction is the untwisted vertex representation of affine Lie algebras of Frenkel-Kac and Segal. Our representation is given by means of a new type of vertex operator corresponding to the simple roots and satisf...
متن کاملTwisted vertex representations of quantum affine algebras
Recent interests in quantum groups are stimulated by their marvelous relations with quantum Yang-Baxter equations, conformal field theory, invariants of links and knots, and q-hypergeometric series. Besides understanding the reason of the appearance of quantum groups in both mathematics and theoretical physics there is a natural problem of finding q-deformations or quantum analogues of known st...
متن کاملLanglands Duality for Finite-dimensional Representations of Quantum Affine Algebras
We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of [6, 4]. We prove this duality for the Kirillov–Reshetikhin modules. In the course of the proof we introduce and construct “interpolating (q, t)-characters” depending on two parameters which interpolate between the q-characte...
متن کامل0 Representations of quantum tori and double - affine Hecke algebras
We study a BGG-type category of infinite dimensional representations of H[W ], a semi-direct product of the quantum torus with parameter q, built on the root lattice of a semisimple group G, and the Weyl group of G. Irreducible objects of our category turn out to be parameterized by semistable G-bundles on the elliptic curve C/q. In the second part of the paper we construct a family of algebras...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2003.06.002