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Bihomogeneous symmetric functions

Published online by Cambridge University Press:  25 May 2021

Yuly Billig*
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada

Abstract

We consider two natural gradings on the space of symmetric functions: by degree and by length. We introduce a differential operator T that leaves the components of this double grading invariant and exhibit a basis of bihomogeneous symmetric functions in which this operator is triangular. This allows us to compute the eigenvalues of T, which turn out to be nonnegative integers.

Type
Article
Copyright
© Canadian Mathematical Society 2021

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Footnotes

Support from the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged.

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