Wed, November 1, 2017
Public Access Category: All |
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- Time:
- 11:00am-12:30pm
- Location:
- Ramanujan Hall
- Description:
- Title: Eigenvalues and eigenvectors of the perfect matching association
scheme.
Abstract:
We revisit the Bose-Mesner algebra of the perfect matching association
scheme (aka the Hecke algebra of the Gelfand pair (S_2n, H_n), where
H_n is the hyperoctahedral group).
Our main results are:
(1) An algorithm to compute the eigenvalues from symmetric group
characters by solving linear equations.
(2) Universal formulas, as content evaluations of symmetric functions,
for the eigenvalues of fixed orbitals (generalizing a result of
Diaconis and Holmes).
(3) An inductive construction of the eigenvectors (generalizing a
result of Godsil and Meagher).