417 citations · 2.1k across the 83 of their papers we have counts for
37 papers · 1 filter
Singular modules for affine Lie algebras, and applications to irregular WZNW conformal blocks
Giovanni Felder, Gabriele Rembado
We give a mathematical definition of spaces of irregular vacua/covacua in genus zero, for any simple Lie algebra, working at generic noncritical level. This uses coinvariants of af…
Baxter operators and asymptotic representations
Giovanni Felder, Huafeng Zhang
We introduce a category of representations of the elliptic quantum group associated with with well-behaved -character theory. We derive separation…
Jointly orthogonal polynomials
Giovanni Felder, Thomas Willwacher
The theory of polynomials orthogonal with respect to one inner product is classical. We discuss the extension of this theory to multiple inner products. Examples include the Lamé a…
On elliptic Calogero-Moser systems for complex crystallographic reflection groups
Pavel Etingof, Giovanni Felder, Xiaoguang Ma +1
To every irreducible finite crystallographic reflection group (i.e., an irreducible finite reflection group G acting faithfully on an abelian variety X), we attach a family of clas…
Deformation quantization with generators and relations
Damien Calaque, Giovanni Felder, Carlo A. Rossi
In this paper we prove a conjecture of B. Shoikhet which claims that two quantization procedures arising from Fourier dual constructions actually coincide.
Bimodules and branes in deformation quantization
Damien Calaque, Giovanni Felder, Andrea Ferrario +1
We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space . The result implies in particular that the Kontsevich deformation quantization…
The character map in deformation quantization
Alberto S. Cattaneo, Giovanni Felder, Thomas Willwacher
The third author recently proved that the Shoikhet-Dolgushev L-infinity-morphism from Hochschild chains of the algebra of smooth functions on manifold to differential forms extends…
On the (ir)rationality of Kontsevich weights
Giovanni Felder, Thomas Willwacher
We compute the weight of a Kontsevich graph in deformation quantization. Up to rationals, the result is Zeta(3)^2/Pi^6.
Equivariant Lefschetz number of differential operators
G. Felder, X. Tang
Let be a compact Lie group acting on a compact complex manifold . We prove a trace density formula for the -Lefschetz number of a differential operator on . We general…
A Riemann-Roch-Hirzebruch formula for traces of differential operators
Markus Engeli, Giovanni Felder
Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n-dimensional compact complex manifold. We prove a formula, conjectured by Feig…
A gerbe for the elliptic gamma function
Giovanni Felder, Andre Henriques, Carlo A. Rossi +1
The identities for elliptic gamma functions discovered by A. Varchenko and one of us are generalized to an infinite set of identities for elliptic gamma functions associated to pai…
Relative formality theorem and quantisation of coisotropic submanifolds
Alberto S. Cattaneo, Giovanni Felder
We prove a relative version of Kontsevich's formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich's theorem if C=M. It states that the…
Density of eigenvalues of random normal matrices
Peter Elbau, Giovanni Felder
The relation between random normal matrices and conformal mappings discovered by Wiegmann and Zabrodin is made rigorous by restricting normal matrices to have spectrum in a bounded…
Hochschild cohomology of the Weyl algebra and traces in deformation quantization
Boris Feigin, Giovanni Felder, Boris Shoikhet
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 or…
Hypergeometric theta functions and elliptic Macdonald polynomials
Giovanni Felder, Alexander Varchenko
Elliptic Macdonald polynomials of sl(2)-type and level 2 are introduced. Suitable limits of elliptic Macdonald polynomials are the standard Macdonald polynomials and conformal bloc…
Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
Alberto S. Cattaneo, Giovanni Felder
General boundary conditions ("branes") for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role play…
Multiplication Formulas for the Elliptic Gamma Function
G. Felder, A. Varchenko
The elliptic gamma function is a generalization of the Euler gamma function. Its trigonometric and rational degenerations are the Jackson q-gamma function and the Euler gamma funct…
Elliptic Selberg integrals and conformal blocks
Giovanni Felder, Laura Stevens, Alexander Varchenko
We present an elliptic version of Selberg's integral formula.
Even powers of divisors and elliptic zeta values
Giovanni Felder, Alexander Varchenko
We introduce and study "elliptic zeta values", a two-parameter deformation of the values of Riemann's zeta function at positive integers. They are essentially Taylor coefficients o…
Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator
G. Felder, L. Stevens, A. Varchenko
We consider the space of elliptic hypergeometric functions of the sl_2 type associated with elliptic curves with one marked point. This space represents conformal blocks in the sl_…
Fedosov connections on jet bundles and deformation quantization
Alberto S. Cattaneo, Giovanni Felder, Lorenzo Tomassini
We review our construction of star-products on Poisson manifolds and discuss some examples. In particular, we work out the relation with Fedosov's original construction in the symp…
q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)
Giovanni Felder, Alexander Varchenko
We study the properties of one-dimensional hypergeometric integral solutions of the q-difference ("quantum") analogue of the Knizhnik-Zamolodchikov-Bernard equations on tori. We sh…
Action of Coxeter groups on m-harmonic polynomials and KZ equations
Giovanni Felder, Alexander P. Veselov
The Matsuo-Cherednik correspondence is an isomorphism from solutions of Knizhnik-Zamolodchikov equations to eigenfunctions of generalized Calogero-Moser systems associated to Coxet…
Elliptic Selberg integrals
Giovanni Felder, Laura Stevens, Alexander Varchenko
We present an elliptic version of Selberg's integral formula.