Related papers: On the Siegel-Weil Theorem for Loop Groups (II)

We develop a theory of loops with involution. On this basis we define a Cayley-Dickson doubling on loops, and use it to investigate the lattice of varieties of loops with involution, focusing on properties that remain valid in the…

We study vector-valued Siegel modular forms of genus 2 and level 2. We describe the structure of certain modules of vector-valued modular forms over rings of scalar-valued modular forms.

Reconstruction theorem for the Moufang loops is proved.

We formulate generalizations of Pauli's theorem on the cases of real and complex Clifford algebras of even and odd dimensions. We give analogues of these theorems in matrix formalism. Using these theorems we present an algorithm for…

Toda equations associated with twisted loop groups are considered. Such equations are specified by Z-gradations of the corresponding twisted loop Lie algebras. The classification of Toda equations related to twisted loop Lie algebras with…

In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular,…

Murray, Roberts and Wockel showed that there is no strict model of the string 2-group using the free loop group. Instead, they construct the next best thing, a coherent model for the string 2-group using the free loop group, with explicit…

We outline an abstract approach to the pseudo-differential Weyl calculus for operators in function spaces in infinitely many variables. Our earlier approach to the Weyl calculus for Lie group representations is extended to the case of…

In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.

We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.

We compute the Weyl group (in the sense of Segal) of the group of holomorphic isometries of a K\"ahler toric manifold with real analytic K\"ahler metric.

We study K-theory classes of Hamiltonian loop group spaces represented by admissible Fredholm complexes. We prove various equivariant index formulae in this context. In a sequel to this article we show that, when specialized to a family of…

In this note, we show the polynomiality of the ring of invariants with respect to the Weyl group of type $A_{2l}^{(2)}$.

We prove Beurling's theorem and $L^p-L^q$ Morgan's theorem for step two nilpotent Lie groups

We prove a duality theorem for quantum groupoid (weak Hopf algebra) actions that extends the well-known result for usual Hopf algebras.

We prove the even isomorphism theorem for Coxeter groups

In part I we introduced the class ${\mathcal E}_2$ of Lie subgroups of $Sp(2,\R)$ and obtained a classification up to conjugation (Theorem 1.1). Here, we determine for which of these groups the restriction of the metaplectic representation…

We calculate certain ext-groups between modules for a linear algebraic group. The results are in agreement with the Lusztig conjecture.

We show a matrix Paley-Wiener theorem for the Hecke algebra of a p-adic group. The proof is based on an analogue of Harish-Chandra's Plancherel formula.

We establish the arithmetic Siegel-Weil formula on the modular curve $\mathcal{X}_{0}(N)$ for arbitrary level $N$, i.e., we relate the arithmetic degrees of special cycles on $\mathcal{X}_{0}(N)$ to the derivatives of Fourier coefficients…