چکیده (انگلیسی):

If one restricts an irreducible representation V λ of GL2nto the orthogonal group (respectively the symplectic group), the trivial representation appears with multiplicity one if and only if all parts of λ are even (resp. the conjugate partition λ’is even). One can rephrase this statement as an integral identity involving Schur functions, the corresponding characters. Rains and Vazirani considered q, t-generalizations of such integral identities, and proved them using affine Hecke algebra techniques. In a recent paper, we investigated the q=0limit (Hall–Little wood), and provided direct combinatorial arguments for these identities; this approach led to various generalizations and a finite-dimensional analog of a recent summation identity of Warnaar. In this paper, we reformulate some of these results using p-adic representation theory; this parallels the representation-theoretic interpretation in the Schur case. The nonzero values of the identities are interpreted as certain p-adic measure counts. This approach provides a p-adic interpretation of these identities (and a new identity), as well as independent proofs. As an application, we obtain a new Little wood summation identity that generalizes a classical result due to Little wood and Macdonald. Finally, our p-adic method also leads to a generalized integral identity