816 research outputs found
Reconstruction and Higher Dimensional Geometry
In this paper, we give a new proof on a Theorem of Tutte which says that the
determinants of the adjacency matrices of two hypomorphic graphs are the same.
We also study the lowest eigenvectors.Comment: 9 pages, to appear in Journal of Combinatorial Theory Series
On Matrix-Valued Square Integrable Positive Definite Functions
In this paper, we study matrix valued positive definite functions on a
unimodular group. We generalize two important results of Godement on square
integrable positive definite functions to matrix valued square integrable
positive definite functions. We show that a matrix-valued continuous
positive definite function can always be written as a convolution of a
positive definite function with itself. We also prove that, given two
matrix valued positive definite functions and , . In addition this integral equals
zero if and only if . Our proofs are operator-theoretic and
independent of the group.Comment: 11 page
Gan-Gross-Prasad Conjecture for U(p,q)
In this paper, we give a proof of the Gan-Gross-Prasad conjecture for the
discrete series of U(p,q). Given a discrete series representation
in terms of the Harish-Chandra parameter, the restriction of to
U(p-1,q) contains as a subrepresentation if and only if and
interlaces in a very special way.Comment: 34 pages, to appear in Inventiones Mathematica
Functions on Symmetric Spaces and Oscillator Representations
We study square integrable functions on the metaplectic group and functions
on the space of unitary symmetric matrices. We relate them using the oscillator
representations.Comment: 25 pages, to appear in Journal of Functional Analysi
Unitary Representations and Theta Correspondence for Type I Classical Groups
In this paper, we prove that theta correspondence preserves unitarity under
certain restrictions.Comment: 25 page
Symmetric Subgroup Actions on Isotropic Grassmannians
Let G be the group preserving a nondegenerate sesquilinear form on a vector
space V, and H a symmetric subgroup of G of the type G1 x G2. We explicitly
parameterize the H-orbits in the Grassmannian of r-dimensional isotropic
subspaces of V by a complete set of H-invariants. We describe the Bruhat order
in terms of the majorization relationship over a diagram of these H-invariants.
The inclusion order, the stabilizer, the orbit dimension, the open H-orbits,
the decompositions of an H orbit into H\cap G_0 and H_0 orbits are also
explicitly described.Comment: 30 page
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