Using the new diffeomorphism invariants of Seiberg and Witten, a uniqueness theorem is proved for Einstein metrics on compact quotients of irreducible 4-dimensional symmetric spaces of non-compact type. The proof also yields a Riemannian version of the Miyaoka-Yau inequality. A smooth Riemannian manifold (M, g) is said [1] to be Einstein if its Ricci curvature is a constant multiple of g. Any i...

The purpose of this note is to announce certain basic results on the construction of a degeneration of M H Xk(n, d) as the smooth curve Xk degenerates to an irreducible nodal curve with a single node. Let Xk be a smooth projective curve of genus g ≥ 2 over an algebraically closed field k of characteristic zero and let L be a line bundle on Xk. A Hitchin pair (E, θ) is comprised of a torsion-fre...

Starting with the superYangian Y (M |N) based on gl(M |N), we define twisted superYangians Y (M |N) ±. Only Y + (M |2n) and Y − (2m|N) can be defined, and appear to be isomorphic one with each other. We study their finite-dimensional irreducible highest weight representations.

We define and study the canonical complex of a finite semidistributive lattice L. It is simplicial on join or meet irreducible elements L which encodes each interval by recording representation its bottom element top element. This behaves properly with respect to quotients L, in sense that quotient subcomplex induced irreducibles uncontracted quotient. then describe combinatorially weak order p...

We calculate the real rank and stable rank of CCR algebras which either have only finite dimensional irreducible representations or have finite topological dimension. We show that either rank of A is determined in a good way by the ranks of an ideal I and the quotient A/I in four cases: When A is CCR; when I has only finite dimensional irreducible representations; when I is separable, of genera...

Let G = GLn(C) and e gln the Grothendieck-Springer resolution of its Lie algebra. Assuming that the zero pre-image μ−1(0) of the moment map μ : T ∗(e gln × Cn) → gln is a complete intersection, we compute its irreducible components. These components dominate components of the corresponding moment pre-image for T (gln×C). We then analyze GIT stability of the irreducible components of μ−1(0) for ...

In the Hopf algebra of symmetric functions, Sym, the basis of Schur functions is distinguished since every Schur function is isomorphic to an irreducible character of a symmetric group under the Frobenius characteristic map. In this note we show that in the Hopf algebra of noncommutative symmetric functions, NSym, of which Sym is a quotient, the recently discovered basis of noncommutative Schur...

In this paper we determine the structure of the natural Ũ(n, n) module Ωp,q(l) which is the Howe quotient corresponding to the determinant character det of U(p, q). We first give a description of the tempered distributions on Mp+q,n(C) which transform according to the character det−l under the linear action of U(p, q). We then show that after tensoring with a character, Ωp,q(l) can be embedded ...

We classify the irreducible, admissible, smooth, genuine mod p representations of the metaplectic double cover of SL2(F ), where F is a p-adic field and p 6= 2. We show, using a generalized Satake transform, that each such representation is isomorphic to a certain explicit quotient of a compact induction from a maximal compact subgroup by an action of a spherical Hecke operator, and we define a...

This paper forms part of a study of 2-arc transitivity for finite imprimitive symmetric graphs, namely for graphs admitting an automorphism groupG that is transitive on ordered pairs of adjacent vertices, and leaves invariant a nontrivial vertex partition B. Such a group G is also transitive on the ordered pairs of adjacent vertices of the quotient graph B corresponding toB. If in additionG is ...