Eng-Chye Tan

Stable branching rules for classical symmetric pairs

We approach the problem of obtaining branching rules from the point of view of dual reductive pairs. Specifically, we obtain a stable branching rule for each of 10 classical families of symmetric pairs. In each case, the branching multiplicities are expressed in terms of Littlewood-Richardson coefficients. Some of the formulas are classical and include, for example, Littlewoods restriction rule as a special case.

Homogeneous functions on light cones: the infinitesimal structure of some degenerate principal series representations

In this paper we study the reducibility, composition series and unitarity of the components of some degenerate principal series representations of

A study of the rank-ambiguity issues in direction-of-arrival estimation

\RMO(p,q)

The explicit duality correspondence of (Sp(p, q), O{*}(2n))

,

Representations of real and p-adic groups

\RMU(p,q)

Counterexamples to a conjecture for characterizing higher rank ambiguities

and

Harmonic analysis, group representations, automorphic forms and invariant theory : in Honor of Roger E. Howe

\SP(p,q)

Quadratic Diophantine equations and two generator Möbius groups

. This is done by realizing these representations in paces of homogeneous functions on light cones and writing down the explicit actions of the universal enveloping algebra of the group concerned.

Invariant Theory of Matrices

We first extend a theorem on linear independence of steering vectors proposed by Godara and Cantoni to include more array-sensor scenarios. We then show that an array can have pairwise linearly independent steering vectors even when all its intersensor spacings are more than /spl lambda//2 where /spl lambda/ is the wavelength of the signals. We next propose a theorem for characterizing rank-2 ambiguity, which is applicable to direction-of-arrival estimation applications where the array sensor locations are fixed and known. Subsequently, we identify a class of three-sensor arrays and a class of uniform circular arrays that have pairwise linearly independent steering vectors and are free of rank-2 ambiguity. We also show that collinearity of sensors, uniformity in intersensor spacings, the dimensions of intersensor spacings, or a combination of some or all of these may give rise to linearly dependent steering vectors. In particular, we demonstrate that for a m-sensor array, m linearly dependent steering vectors exist if the aperture is greater than [(m-1)/2]/spl lambda//2, or when at least ([(m+1)/2]+1) sensors are collinear.

Poincaré series of holomorphic representations

Abstract We investigate the type I dual pairs over the quaternion algebra H , namely the family of dual pairs (Sp(p,q),O ∗ (2n)) . We give a complete and explicit description of duality correspondence for p + q ⩽ n as well as some of the cases for p + q > n , in terms of the Langlands parameters.