Hung Yean Loke

Howe quotients of unitary characters and unitary lowest weight modules

In this paper, let (G,G′) be the dual pair (Sp(p,R), O(n,m)). We will determine the composition series of the Howe quotients of G′ which are lifts from one dimensional unitary representations of G and unitary lowest weight modules of G. We will also determine the unitarizability of the subquotients. Our method also works for the dual pairs (Ũ(p, q), Ũ(n,m)) and (O∗(2p), Sp(n,m)). Research partially funded by the NUS Academic Research Grant R-146-000-026-112. Research partially funded by the NUS Academic Research Grant R-146-000-026-112. 1991 Mathematics Subject Classification. 22E46, 22E47.

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

Rank and matrix coefficients for simply laced groups

L \cong M \times U

Degenerate principal series representations of Sp(p, q)

where

Restrictions of Quaternionic Representations

\left( {M,U} \right) = \left\{ \begin{gathered} \left( {GL_q \left( \mathbb{C} \right),U\left( {p - q} \right)} \right),{ }if G = U\left( {p,q} \right){,} \hfill \\ \left( {GL_q^{ + } \left( \mathbb{R} \right), Spin\left( {p - q} \right)} \right),{ } if G = Spin_0 \left( {p,q} \right). \hfill \\ \end{gathered} \right.

On minimal representations of Chevalley groups of type Dn, En and G2

Let χ be a one-dimensional character of M and τμ an irreducible representation of U with highest weight μ. Let