Related papers: Equivariant correspondences and the Borel-Bott-Wei…

We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.

For a compact simply connected simple Lie group $G$ with an involution $\alpha$, we compute the $G\rtimes \Z/2$-equivariant K-theory of $G$ where $G$ acts by conjugation and $\Z/2$ acts either by $\alpha$ or by $g\mapsto \alpha(g)^{-1}$. We…

Let $G$ be a connected semi-simple group defined over and algebraically closed field, $T$ a fixed Cartan, $B$ a fixed Borel containing $T$, $S$ a set of simple reflections associated to the simple positive roots corresponding to $(T,B)$,…

We establish a noncommutative generalisation of the Borel-Weil theorem for the Heckenberger-Kolb calculi of the irreducible quantum flag manifolds $\mathcal{O}_q(G/L_S)$, generalising previous work of a number of authors (including the…

We characterize having Borel isomorphism relation among some weakly minimal trivial theories, namely the examples of families of finite equivalence relations from recent joint work with Laskowski, and tame expansions of…

The aim of this text is to give an explicit formula for the restriction to fixed points of a basis of the equivariant K-theory of the flag varieties and of the Bott-Samelson varieties.

We prove a Seidel product formula for the torus-equivariant quantum $K$-theory of a generalized flag variety $G/P.$ This is a natural generalization of the corresponding results by Buch, Chaput, and Perrin for the cominuscule flag…

We prove in this paper a Borel-Weil-Bott type theorem for the coHochschild homology of a quantum shuffle algebra associated with quantum group datum taking coefficients in some well-chosen bicomodules, which can be looked as an analogue of…

Let G be a simple simply connected complex algebraic group. We give a Lie theoretic construction of a conjectural mirror family associated to a general flag variety G/P, and show that it recovers the Peterson variety presentation for the…

For an $r$-discrete Hausdorff groupoid ${\cal G}$ and an inverse semigroup $S$ of slices of ${\cal G}$ there is an isomorphism between ${\cal G}$-equivariant $KK$-theory and compatible $S$-equivariant $KK$-theory. We use it to define…

We give a combinatorial Chevalley formula for an arbitrary weight, in the torus-equivariant K-theory of semi-infinite flag manifolds, which is expressed in terms of the quantum alcove model. As an application, we prove the Chevalley formula…

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 give a Chevalley formula for an arbitrary weight for the torus-equivariant $K$-group of semi-infinite flag manifolds, which is expressed in terms of the quantum alcove model. As an application, we prove the Chevalley formula for an…

Let G --> G' be an embedding of semisimple complex Lie groups, let B and B' be a pair of nested Borel subgroups, and let f:G/B --> G'/B' be the associated equivariant embedding of flag manifolds. We study the pullbacks of cohomologies of…

We prove an identity for (torus-equivariant) 3-point, genus 0, $K$-theoretic Gromov-Witten invariants of flag manifolds $G/P$, which can be thought of as a replacement for the ``divisor axiom'' in their (torus-equivariant) quantum…

We establish a theorem computing the cohomology groups of line bundles on homogeneous ind-varieties $G/B$ for diagonal ind-groups $G$. The main difficulty in proving this analog of the classical Bott-Borel-Weil theorem is in defining an…

Using the description of the category of quasi-coherent sheaves on a root stack given in the paper of N. Borne and A. Vistoli, we study the G-theory of root stacks via localisation methods. We apply our results to the study of equivariant…

We study equivariant contact structures on complex projective varieties arising as partial flag varieties $G/P$, where $G$ is a connected, simply-connected complex simple group of type $ADE$ and $P$ is a parabolic subgroup. We prove a…

We use correspondences to define a purely topological equivariant bivariant K-theory for spaces with a proper groupoid action. Our notion of correspondence differs slightly from that of Connes and Skandalis. We replace smooth K-oriented…

We give a Borel-type presentation of the torus-equivariant (small) quantum $K$-ring of flag manifolds of type $C$.