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Automorphic properties of generating functions for generalized rank moments and Durfee symbols
, 2009
"... We define twoparameter generalizations of two combinatorial constructions of Andrews: the kth symmetrized rank moment and the kmarked Durfee symbol. We prove that three specializations of the associated generating functions are socalled quasimock theta functions, while a fourth specialization gi ..."
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We define twoparameter generalizations of two combinatorial constructions of Andrews: the kth symmetrized rank moment and the kmarked Durfee symbol. We prove that three specializations of the associated generating functions are socalled quasimock theta functions, while a fourth specialization gives quasimodular forms. We then define a twoparameter generalization of Andrews’ smallest parts function and note that this leads to quasimock theta functions as well. The automorphic properties are deduced using qseries identities relating the relevant generating functions to known mock theta functions.
DILOGARITHM IDENTITIES FOR CONFORMAL FIELD THEORIES AND CLUSTER ALGEBRAS: Simply Laced Case
, 2010
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Fermionic expressions for the characters of c(p,1) logarithmic conformal field theories
 Nucl. Phys. B
"... We present fermionic quasiparticle sum representations consisting of a single fundamental fermionic form for all characters of the logarithmic conformal field theory models with central charge cp,1, p ≥ 2, and suggest a physical interpretation. We also show that it is possible to correctly extract ..."
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Cited by 13 (2 self)
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We present fermionic quasiparticle sum representations consisting of a single fundamental fermionic form for all characters of the logarithmic conformal field theory models with central charge cp,1, p ≥ 2, and suggest a physical interpretation. We also show that it is possible to correctly extract dilogarithm identities.
Higgs bundles, gauge theories and quantum groups
 Commun. Math. Phys
"... The appearance of the Bethe Ansatz equation for the Nonlinear Schrödinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions of the corresponding twodimensional topological U(N) gauge theory reproduce quantum wave functions ..."
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Cited by 10 (1 self)
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The appearance of the Bethe Ansatz equation for the Nonlinear Schrödinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions of the corresponding twodimensional topological U(N) gauge theory reproduce quantum wave functions of the Nonlinear Schrödinger equation in the Nparticle sector. This implies the full equivalence between the above gauge theory and the Nparticle subsector of the quantum theory of Nonlinear Schrödinger equation. This also implies the explicit correspondence between the gauge theory and the representation theory of degenerate double affine Hecke algebra. We propose similar construction based on the G/G gauged WZW model leading to the representation theory of the double affine Hecke algebra. The relation with the Nahm transform and the geometric Langlands correspondence is briefly discussed
A REFINED BLOCH GROUP AND THE THIRD HOMOLOGY OF SL2 OF A FIELD
"... Abstract. We use the properties of the refined Bloch group to prove that H3 of SL2 of a global field is never finitelygenerated, and to calculate H3 of SL2 of local fields with odd residue characteristic up to some 2torsion. We also give lower bounds for the 3rank of the homology groups H3(SL2(OS ..."
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Cited by 7 (6 self)
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Abstract. We use the properties of the refined Bloch group to prove that H3 of SL2 of a global field is never finitelygenerated, and to calculate H3 of SL2 of local fields with odd residue characteristic up to some 2torsion. We also give lower bounds for the 3rank of the homology groups H3(SL2(OS),Z).
Integrable deformations of CFTs and the discrete Hirota equations
, 905
"... One of the current major targets in physics is the understanding of integrable quantum field theories in two dimensions. In theories with diagonal scattering matrix there is a convincing conjecture for the spectrum of the Hamiltonian. Suppose that there are K species of particles with masses ma, a = ..."
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Cited by 7 (0 self)
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One of the current major targets in physics is the understanding of integrable quantum field theories in two dimensions. In theories with diagonal scattering matrix there is a convincing conjecture for the spectrum of the Hamiltonian. Suppose that there are K species of particles with masses ma, a = 1,...,K, and a
Periodicities Of T and YSystems, DILOGARITHM IDENTITIES, AND CLUSTER ALGEBRAS I: Type Br
, 2010
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