$K$-type multiplicities in degenerate principal series via Howe duality

Mark Colarusso, William Q. Erickson, Andrew Frohmader +1

Let $K$ be one of the complex classical groups ${\mathrm{O}}_k$, ${\mathrm{GL}}_k$, or ${\mathrm{Sp}}_{2k}$. Let $M\subseteq K$ be the block diagonal embedding ${\rm O}_{k_1} \times \cdots \time…