Related papers: Borel-Weil-Bott theory for Loop Groups

We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.

A fundamental problem at the confluence of algebraic geometry and representation theory is to describe the cohomology of line bundles on flag varieties over a field of characteristic p. When p=0, the solution is given by the celebrated…

We formulate and prove the Siegel-Weil formula for loop groups.

We prove an analogue of the Borel-Bott-Weil theorem in equivariant KK-theory by constructing certain canonical equivariant correspondences between minimal flag varieties G/B, with G a complex semisimple Lie group.

We compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold. This is applied to (1) finding the character of $G$-integrable irreducible highest weight modules over the affine Lie…

We give a branching law for subgroups fixed by an involution. As an application we give a generalization of the Cartan-Helgason theorem and a noncompact analogue of the Borel-Weil theorem.

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…

The Borel-Weil-Bott theorem describes the cohomology of line bundles over flag varieties. Here, one generalizes this theorem to a wider class of projective varieties : the wonderful varieties of minimal rank.

Let G be a locally compact abelian group with compact open subgroup H. The best known example of such a group is G=Q_p, the field of p-adic rational numbers (as a group under addition), which has compact open subgroup H=Z_p, the ring of…

We study the cohomology groups of tautological bundles on Quot schemes over the projective line, which parametrize rank $r$ quotients of a vector bundle $V$ on $\mathbb{P}^1$. Our main result is an analogue of the Borel--Weil--Bott theorem…

In the present notes we generalize the classical work of Demazure [Invariants sym\'etriques entiers des groupes de Weyl et torsion] to arbitrary oriented cohomology theories and formal group laws. Let G be a split semisemiple linear…

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…

We derive a discrete analogue of Morse-Bott theory on CW complexes and use this discrete Morse-Bott function to do some Conley theory analysis. It turns out that our discrete Morse-Bott theory is indeed a generalization of Forman's discrete…

This article will explore the K- and L-theory of group rings and their applications to algebra, geometry and topology. The Farrell-Jones Conjecture characterizes K- and L-theory groups. It has many implications, including the Borel and…

The celebrated Borel--Tits theorem provides a classification of abstract isomorphisms between (simple) isotropic groups over fields, showing that such isomorphisms arise from field isomorphisms and group-scheme isomorphisms. In this work,…

In this paper, we consider affine Deligne-Lusztig varieties $X_w(b)$ and their certain union $X(\mu,b)$ inside the affine flag variety of a reductive group. Several important results in the study of affine Deligne-Lusztig varieties have…

We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and…

We analyse abelian T-duality for WZW models of simply-connected groups. We demonstrate that the dual theory is a certain orbifold of the original theory, and check that it is conformally invariant. We determine the spectrum of the dual…

Let G be a connected reductive complex algebraic group and B a Borel subgroup of G. We consider a subgroup H of B acting with finitely many orbits on the flag variety G/B, and we classify the H-orbits in G/B in terms of suitable…

We describe the action of the Weyl group of a semi simple linear group $G$ on cohomological and K-theoretic invariants of the generalized flag variety $G/B$. We study the automorphism $s_i$, induced by the reflection in the simple root, on…