Hall-Littlewood Polynomial
المؤلف:
Fulman, J.
المصدر:
"The Rogers-Ramanujan Identities, the Finite General Linear Groups, and the Hall-Littlewood Polynomials." Proc. Amer. Math. Soc. 128
الجزء والصفحة:
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18-9-2019
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Hall-Littlewood Polynomial
Let 
be an integer such that 
, where 
is a partition of 
if 
, where 
are a sequence of positive integers stabilizing 0 such that 
. Also let 
be the number of parts of 
of size 
. Then the permutation 
, where 
is the symmetric group, acts on the variables 
, ..., 
by sending 
to 
. Letting 
be a complex number, the Hall-Littlewood polynomials are defined by
These polynomials interpolate between the Schur functions (with 
) and the monomial symmetric functions (with 
; Fulman 1999).
REFERENCES:
Fulman, J. "The Rogers-Ramanujan Identities, the Finite General Linear Groups, and the Hall-Littlewood Polynomials." Proc. Amer. Math. Soc. 128, 17-25, 1999.
Macdonald, I. G. Symmetric Functions and Hall Polynomials, 2nd ed. Oxford, England: Oxford University Press, p. 208, 1995.
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