567 research outputs found
Representation Theory of The Algebra
We review the recent development in the representation theory of the
algebra. The topics that we concern are, Quasifinite
representation, Free field realizations, (Super) Matrix Generalization,
Structure of subalgebras such as algebra, Determinant formula,
Character formula. (Invited talk at ``Quantum Field Theory, Integrable Models
and Beyond", YITP, 14-17 February 1994. To appear in Progress of Theoretical
Physics Proceedings Supplement.)Comment: 36 pages, LaTeX, RIMS-990, YITP/K-1087, YITP/U-94-25, SULDP-1994-
Macdonald operators and homological invariants of the colored Hopf link
Using a power sum (boson) realization for the Macdonald operators, we
investigate the Gukov, Iqbal, Kozcaz and Vafa (GIKV) proposal for the
homological invariants of the colored Hopf link, which include
Khovanov-Rozansky homology as a special case. We prove the polynomiality of the
invariants obtained by GIKV's proposal for arbitrary representations. We derive
a closed formula of the invariants of the colored Hopf link for antisymmetric
representations. We argue that a little amendment of GIKV's proposal is
required to make all the coefficients of the polynomial non-negative integers.Comment: 31 pages. Published version with an additional appendi
Quantum Algebras and Macdonald Polynomials
We derive a quantum deformation of the algebra and its quantum Miura
transformation, whose singular vectors realize the Macdonald polynomials.Comment: LaTeX file, 17-pages, no-figures, a reference adde
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