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Consider the symmetric pair $(\textbf{GL}_n, \textbf{O}_n)$ in the setting ofthe Kostant-Rallis Theorem. We provide a combinatorial formula for the gradedmultiplicity of an irreducible $\textbf{O}_n$-representation in the harmonicpolynomials on $\mathfrak{p}$. The results here are expected to extend to theother classical symmetric pairs.

Graded Multiplicities in the Kostant-Rallis Setting