Related papers: How to sheafify an elliptic quantum group
Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups K^G_*(X), using an obvious equivariant version of the (M,E,f)-picture of Baum-Douglas for K-homology. We define explicit natural…
The present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable Kac-Moody algebras. The resulting quantum symmetric pairs are right coideal subalgebras…
For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and…
We describe quantum enveloping algebras of symmetric Kac-Moody Lie algebras via a finite field Hall algebra construction involving Z_2-graded complexes of quiver representations.
In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map. We develop…
Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten…
We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…
Let $\hat{\mathfrak{g}}$ be an untwisted affine Kac-Moody algebra, with its Sklyanin-Drinfel'd structure of Lie bialgebra, and let $\hat{\mathfrak{h}}$ be the dual Lie bialgebra. By dualizing the quantum double construction - via formal…
As a natural generalization quantum Schur algebras associated with the Hecke algebra of the symmetric group, we introduce the quantum Schur superalgebra of type Q associated with the Hecke-Clifford superalgebra, which, by definition, is the…
In this paper we prove that the etale sheafification of the functor arising from the quotient of an algebraic supergroup by a closed subsupergroup is representable by a smooth superscheme.
We calculate equivariant elliptic cohomology of the partial flag variety G/H, where H \subseteq G are compact connected Lie groups of equal rank. We identify the RO(G)-graded coefficients Ell_G^* as powers of Looijenga's line bundle and…
We show how the modular symmetries that have been found to be consistent with most available scaling data from quantum Hall systems, derive from a rigid family of algebraic curves of the elliptic type. The complicated special functions…
We construct twisted $\mathcal{D}$-modules on the projective line $\mathbb{P}^1$ that are equivariant for the action of the diagonal torus subgroup of $SL_2$. In the most interesting case these arise as extensions from local systems on…
A vertex-algebraic analogue of the Lie algebroid complex is constructed, which generalizes the "small" chiral de Rham complex on smooth manifolds. The notion of VSA-inductive sheaves is also introduced. This notion generalizes that of…
We define an elliptic version of the stable envelope of Maulik and Okounkov for the equivariant elliptic cohomology of cotangent bundles of Grassmannians. It is a version of the construction proposed by Aganagic and Okounkov and is based on…
The interplay between equivariant stable homotopy theory and spectral algebraic geometry is used to construct a derived Tate curve over $\mathrm{KU}((q))$, a lift of the classical elliptic curve of Tate over $\mathbf{Z}((q))$. Applications…
The search for elliptic quantum groups leads to a modified quantum Yang-Baxter relation and to a special class of quasi-triangular quasi Hopf algebras. This paper calculates deformations of standard quantum groups (with or without spectral…
We report some observations concerning two well-known approaches to construction of quantum groups. Thus, starting from a bialgebra of inhomogeneous type and imposing quadratic, cubic or quartic commutation relations on a subset of its…
We survey the well-known Yangian of $\widehat{\mathfrak{gl}}_1$ /quantum toroidal $\mathfrak{gl}_1$ action on the cohomology / $K$-theory of moduli spaces of stable sheaves on surfaces, and give the generalization of this construction to…
We show that the vector bundle on the moduli stack $M_\mathrm{ell}$ of elliptic curves associated to the $2$-cell complex $C\nu$ is isomorphic to the de Rham cohomology sheaf $\mathrm{H}^1_\mathrm{dR}(\mathcal{E}/M_\mathrm{ell})$ of the…