Highest weight irreducible representations of the quantum algebra Uh(A∞)
نویسندگان
چکیده
منابع مشابه
Highest weight representations of the Virasoro algebra
We consider representations of the Virasoro algebra, a one-dimensional central extension of the Lie algebra of vectorfields on the unit circle. Positive-energy, highest weight and Verma representations are defined and investigated. The Shapovalov form is introduced, and we study Kac formula for its determinant and some consequences for unitarity and degeneracy of irreducible highest weight repr...
متن کاملHIGHEST WEIGHT VECTORS OF IRREDUCIBLE REPRESENTATIONS OF THE QUANTUM SUPERALGEBRA Uq (gl(m,n))
The Iwahori-Hecke algebra Hk(q ) of type A acts on tensor product space V ⊗k of the natural representation of the quantum superalgebra Uq(gl(m, n)). We show this action of Hk(q ) and the action of Uq(gl(m, n)) on the same space determine commuting actions of each other. Together with this result and Gyoja’s q-analogue of the Young symmetrizer, we construct a highest weight vector of each irredu...
متن کاملREPRESENTATIONS OF THE QUANTUM TOROIDAL ALGEBRA ON HIGHEST WEIGHT MODULES OF THE QUANTUM AFFINE ALGEBRA OF TYPE gl N
A representation of the quantum toroidal algebra of type sl N is de ned on every integrable irreducible highest weight module of the the quantum a ne algebra of type gl N : The q-version of the level-rank duality giving the reciprocal decomposition of the q-Fock space with respect to mutually commutative actions of U 0 q ( b gl N ) of level L and U 0 q ( b sl L ) of level N is described.
متن کاملCHARACTERS OF THE IRREDUCIBLE REPRESENTATIONS WITH FUNDAMENTAL HIGHEST WEIGHT FOR THE SYMPLECTIC GROUP IN CHARACTERISTIC p
Abstract. Let K be an algebraically closed field of characteristic p > 0 and let Sp(2m) be the symplectic group of rank m over K. The main theorem of this article gives the character of the rational simple Sp(2m)-modules with fundamental highest weight as an explicit alternating sum of characters of Weyl modules. One obtains several formulae for the dimensions of these simple modules, what allo...
متن کاملDetails of the Non-Unitarity Proof for Highest Weight Representations of the Virasoro Algebra
We give an exposition of the details of the proof that all highest weight representations of the Virasoro algebra for c < 1 which are not in the discrete series are non-unitary. The Virasoro algebra is the infinite dimensional Lie algebra with generators Ln, neZ, satisfying the commutation relations lK>^ = (TM-n)Lm+n+^c(m 3-m)δm+nt0. (1) The number c is called the central charge. The Verma modu...
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 Mathematical Physics
سال: 1998
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.532597