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This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a puncturedsphere with fixedlocal monodromy. The submanifoldis definedvia products of inv...
UNITARY SHIMURA CORRESPONDENCES FOR SPLIT REAL GROUPS.
Unitary representations of real reductive groups     Unitary representations  real reductive groups       font style='font-size:12px;'> 2015/9/28
The purpose of this paper is to give a finite algorithm for computing the set of irreducible unitary representations of a real reductive Lie group G. Even before explaining the nature of the algorithm...
Unitary Spherical Dual, Split Groups     Unitary Spherical Dual  Split Groups       font style='font-size:12px;'> 2015/8/17
De nition 2.0.1. A representation (;X) on a Hilbert space X is called unitary if X admits a (nondegenerate) inner product h ; i such that G acts by unitary transformations.
This talk is about aspects of representation theory of p􀀀adic groups that parallel real groups. In the case of real groups, the results refer to J. Adams, P. Trapa, M. vanLeuwen, W-L. Yee a...
This talk is about aspects of representation theory of p􀀀adic groups that parallel real groups. This conforms to the Lefschetz principle which states that what is true for real groups is al...
Spherical Unitary dual for quasisplit real groups     quasisplit real groups  Spherical Unitary       font style='font-size:12px;'> 2015/8/17
G is the real points of a linear connected reductive group. - g0 := Lie(G),  Cartan involution, g0 = k0 + s0, g := (g0)C, K maximal compact subgroup, g = k + s, - P = MAN minimal parabolic subgrou...
SPHERICAL UNITARY DUAL FOR COMPLEX CLASSICAL GROUPS     CLASSICAL GROUPS  SPHERICAL UNITARY DUAL       font style='font-size:12px;'> 2015/8/17
The full unitary dual for the complex classical groups viewed as real Lie groups is computed in [B1]. This was close to 20 years ago. Since then there have been many advances, but the general proble...
1.1. Positive de nite functions. We start with the classical notion of positive de nite functions. De nition. A continuous function f : R 􀀀! C is called positive de nite if it satis es (1...
This paper presents some new statistical tests and new conjectures regarding the correspondence between the eigenvalues of random unitary matrices and the zeros of Riemann’s zeta function. Global fe...
We prove that crystalline points are dense in the spectrum of the completed Hecke algebra on unitary Shimura varieties.
Arthur has conjectured that the unitarity of a number of representations can be shown by finding appropriate automorphic realizations. This has been verified for classical groups by Moeglin and for th...
We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of totally isotropic subspa...
Almost commuting unitary matrices related to time reversal     unitary matrices  time reversal  Operator Algebras       font style='font-size:12px;'> 2011/9/16
Abstract: The behavior of fermionic systems depends on the geometry of the system and the symmetry class of the Hamiltonian and observables. Almost commuting matrices arise from band-projected positio...
Abstract: Given a purely contractive matrix-valued analytic function $\Theta$ on the unit disc $\bm{D}$, we study the $\mc{U} (n)$-parameter family of unitary perturbations of the operator $Z_\Theta$ ...

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