Related papers: On the Siegel-Weil Theorem for Loop Groups (II)
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.
We study the Siegel-Weil formula in the second term range ($n+1\leq m\leq n+r$) for unitary groups of hermitian forms over a skew-field $D$ with involution of the second kind.
We give an elementary proof of the group law for elliptic curves using explicit formulas.
This note outlines the Borel-Weil-Bott theory for (arbitrary-genus) flag varieties of loop groups, following ideas of G. Segal. Recent revivalist interest in the "WZW fusion rules" suggests that my original (CMP 1995) treatment of the…
I calculate characters of certain representations of loop groups based on non simply connected Lie groups. This gives a generalization of the Kac-Weyl character formula.
In this paper, we prove a Liouville theorem for the $2$-Hessian equation on the Heisenberg group $\mathbb{H}^n$. The result is obtained by choosing a suitable test function and using integration by parts to derive the necessary integral…
In the spirit of an earlier result of M\"uller on the Heisenberg group we prove a restriction theorem on a certain class of two step nilpotent Lie groups. Our result extends that of M\"uller also in the framework of the Heisenberg group.
We will give the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group explicitly.
We describe Steiner loops of nilpotency class 2 and establish the classification of finite 3-generated nilpotent Steiner loops of nilpotency class 2.
We derive Verlinde's formula from the fixed point formula for loop groups proved in the companion paper "A fixed point formula for loop group actions", and extend it to compact, connected groups that are not necessarily simply-connected.
We establish a Siegel-Weil formula for classical groups over a function field with odd characteristic, which asserts in many cases that the Siegel Eisenstein series is equal to an integral of a theta function. This is a function-field…
We give an elementary proof of the reducedness of twisted loop groups along the lines of the Kneser-Tits problem.
In this paper, we focus on Oliver's $p$-group conjecture. We use elementary method to prove that Oliver's $p$-group conjecture holds for Sylow $p$-subgroups of unitary groups.
We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.
We prove the conjugacy of Sylow $p$-subgroups of linear pseudofinite groups under the assumption of the existence of a finite Sylow $p$-subgroup. We also give an example of a linear pseudofinite group with non-conjugate Sylow $2$-subgroups.
We compute higher moments of the Siegel--Veech transform over quotients of $SL(2,\mathbb{R})$ by the Hecke triangle groups. After fixing a normalization of the Haar measure on $SL(2,\mathbb{R})$ we use geometric results and linear algebra…
We prove the higher Siegel--Weil formula for \emph{corank one} terms, relating (1) the $r^{\rm th}$ central derivatives of corank one Fourier coefficients of Siegel--Eisenstein series, and (2) the degrees of special cycles of virtual…
We prove a recursive formula for the exterior and symmetric powers of modules for a cyclic 2-group. This makes computation straightforward. Previously, a complete description was only known for cyclic groups of prime order.
Second-order equations of motion on a group manifold that appear in a large class of so-called chiral theories are presented. These equations are presented and explicitely solved for cases of semi-simple, finite-dimensional Lie groups. With…
We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.