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AFFINE KAC-MOODY ALGEBRAS AT THE CRITICAL LEVEL AND GELFAND-DIKII ALGEBRAS
We prove Drinfeld's conjecture that the center of a certain completion of the universal enveloping algebra of an affine Kac-Moody algebra at the critical level is isomorphic to the Gelfand-DikiiExpand
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Additive K-theory
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A commutative algebra on degenerate CP1 and Macdonald polynomials
We introduce a unital associative algebra A associated with degenerate CP1. We show that A is a commutative algebra and whose Poincare series is given by the number of partitions. Thereby, we canExpand
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QuantumOpen image in new window-algebras and elliptic algebras
We define a quantum Open image in new window -algebra associated to\(\mathfrak{s}\mathfrak{l}_N \) as an associative algebra depending on two parameters. For special values of the parameters, thisExpand
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Quantization of the Drinfeld-Sokolov reduction
Abstract We show that the quantum Drinfeld-Sokolov reduction of the affine Kac-Moody algebra sl( n ) Λ gives the W n -algebra of Fateev-Zamolodchikov-Lukyanov. We derive this W n -algebra explicitlyExpand
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Gaudin model, Bethe Ansatz and critical level
We propose a new method of diagonalization oif hamiltonians of the Gaudin model associated to an arbitrary simple Lie algebra, which is based on the Wakimoto modules over affine algebras at theExpand
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Super Liouville conformal blocks from $ \mathcal{N} = 2 $ SU(2) quiver gauge theories
The conjecture about the correspondence between instanton partition functions in the N = 2 SUSY Yang-Mills theory and conformal blocks of two-dimensional conformal field theories is extended to theExpand
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Quantum-algebras and elliptic algebras
AbstractWe define a quantum-algebra associated to $$\mathfrak{s}\mathfrak{l}_N $$ as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomesExpand
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Hochschild cohomology of the Weyl algebra and traces in deformation quantization
We give a formula for a cocycle generating the Hochschild cohomology of the Weyl algebra with coefficients in its dual.It is given by an integral over the configuration space of ordered points on aExpand
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A differential ideal of symmetric polynomials spanned by Jack polynomials at rβ = -(r=1)/(k+1)
For each pair of positive integers (k,r) such that k+1,r-1 are coprime, we introduce an ideal $I^{(k,r)}_n$ of the ring of symmetric polynomials. The ideal $I^{(k,r)}_n$ has a basis consisting ofExpand
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