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Traces of intertwiners for quantum groups and difference equations, I
 DUKE MATHEMATICAL JOURNAL
, 2000
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On the center of quantized enveloping algebras
 J. Alg
, 1998
"... Let U be a quasitriangular Hopf algebra. One may use the Rmatrix of U in order to construct scalar invariants of knots. Analogously, Reshetikhin wrote tangle invariants which take their values in the center of U. Reshetikhin’s expressions thus define central elements in U. We prove here an identity ..."
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Let U be a quasitriangular Hopf algebra. One may use the Rmatrix of U in order to construct scalar invariants of knots. Analogously, Reshetikhin wrote tangle invariants which take their values in the center of U. Reshetikhin’s expressions thus define central elements in U. We prove here an identity caracterizing some of these elements, when U is a quantized enveloping algebra. As an application, we give a proof for a statement of Faddeev, Reshetikhin and Takhtadzhyan concerning the center of a quantized enveloping algebra.
Theta functions associated with affine root systems and the elliptic Ruijsenaars operators
 Physical Combinatorics, Birkhauser
"... We study a family of mutually commutative difference operators associated with the affine root systems. These operators act on the space of meromorphic functions on the Cartan subalgebra of the affine Lie algebra. We show that the space spanned by the characters of a fixed positive level is invarian ..."
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We study a family of mutually commutative difference operators associated with the affine root systems. These operators act on the space of meromorphic functions on the Cartan subalgebra of the affine Lie algebra. We show that the space spanned by the characters of a fixed positive level is invariant under the action of these operators. Email:
Twisted traces of quantum intertwiners and quantum dynamical Rmatrices corresponding to . . .
, 2000
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CENTER AND UNIVERSAL RMATRIX FOR QUANTIZED BORCHERDS SUPERALGEBRAS
, 1998
"... Abstract. We construct a nondegenerate symmetric bilinear form on quantized enveloping algebras associated to Borcherds superalgebras. With this, we study its center and its universal Rmatrix. 1. ..."
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Abstract. We construct a nondegenerate symmetric bilinear form on quantized enveloping algebras associated to Borcherds superalgebras. With this, we study its center and its universal Rmatrix. 1.
An MTheoretic Derivation of a 5d and 6d AGT Correspondence, and Relativistic and Elliptized Integrable Systems
"... We generalize our analysis in [arXiv:1301.1977], and show that a 5d and 6d AGT correspondence for SU(N) – which essentially relates the relevant 5d and 6d Nekrasov instanton partition functions to the integrable representations of a qdeformed and elliptic affine WNalgebra – can be derived, purel ..."
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We generalize our analysis in [arXiv:1301.1977], and show that a 5d and 6d AGT correspondence for SU(N) – which essentially relates the relevant 5d and 6d Nekrasov instanton partition functions to the integrable representations of a qdeformed and elliptic affine WNalgebra – can be derived, purely physically, from the principle that the spacetime BPS spectra of stringdual Mtheory compactifications ought to be equivalent. Via an appropriate defect, we also derive a “fullyramified ” version of the 5d and 6d AGT correspondence where integrable representations of a quantum and elliptic affine SU(N)algebra at the critical level appear on the 2d side, and argue that the relevant “fullyramified ” 5d and 6d Nekrasov instanton partition functions are simultaneous eigenfunctions of commuting operators which define relativistic and elliptized integrable systems. As an offshoot, we also obtain various mathematically novel and interesting relations involving the double loop algebra of SU(N), elliptic Macdonald operators, equivariant elliptic genus of instanton moduli space, and more. ar X iv