Alladi Ramakrishnan Hall
Eigenvalues and Eigenvectors of the perfect matching association scheme
Murali K. Srinivasan
IIT Bombay
We revisit the Bose-Mesner algebra of the perfect matching scheme or, equivalently, the Hecke algebra of the Gelfand pair $(S_2n, H_n)$ ($H_n$ = hyperoctahedral group). Our main results are:
(i) An algorithm for the eigenvalues from symmetric group characters by solving linear equations.
(ii) Universal formulas, as content evaluations of symmetric functions, for the eigenvalues of fixed orbitals (generalizing
a result of Diaconis and Holmes).
(iii) Inductive construction of the eigenvectors (generalizing a result of Godsil and Meagher).
Done