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Wednesday, November 8, 2017
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November 2017
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11:00am [11:00am]Murali Srinivasan
Description:
Combinatorics Seminar Title: Eigenvalues and eigenvectors of the perfect matching association scheme. (Part II) 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).

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