Soo Teck Lee

Degenerate principal series and local theta correspondence

Following our previous paper [LZ] which deals with the groupU(n, n), we study the structure of certain Howe quotients Ω p,q and Ω p,q (1) which are natural Sp(2n,R) modules arising from the Oscillator representation associated with the dual pair (O(p, q), Sp(2n,R)), by embedding them into the degenerate principal series representations of Sp(2n,R) studied in [L2].

Degenerate principal series and local theta correspondence II

Following our previous paper [LZ] which deals with the groupU(n, n), we study the structure of certain Howe quotients Ωp,q and Ωp,q(1) which are natural Sp(2n,R) modules arising from the Oscillator representation associated with the dual pair (O(p, q), Sp(2n,R)), by embedding them into the degenerate principal series representations of Sp(2n,R) studied in [L2].

Why should the Littlewood–Richardson Rule be true?

We give a proof of the Littlewood-Richardson Rule for describing tensor products of irreducible finite-dimensional representations of GLn. The core of the argument uses classical invariant theory, especially (GLn,GLm)duality. Both of the main conditions (semistandard condition, lattice permutation/Yamanouchi word condition) placed on the tableaux used to define Littlewood-Richardson coefficients have natural interpretations in the argument.

Bases for some reciprocity algebras I

For a complex vector space V, let P(V) be the algebra of polynomial functions on V. In this paper, we construct bases for the algebra of all GL n (C) x GL m1 (C) x GL m2 (C) x ... x GL mr (C) highest weight vectors in P (C n ⊗ C m ), where m = m 1 +... + m r and mj < n for all 1 < j < r, and the algebra of GL n (C) x GL k (C) x GL 1 (C) highest weight vectors in P [(C n ⊗ C k ) ⊕ (C n * ⊗ C l )].

Degenerate Principal Series Representations of U(p, q) and Spin0(p, q)

AbstractLet p>q and let G be the group U(p, q) or Spin0(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup

Double Pieri algebras and iterated Pieri algebras for the classical groups

L \cong M \times U

A reciprocity law and the skew Pieri rule for the symplectic group

where