282 research outputs found
Generating functions for the universal Hall-Littlewood - and -functions
Recently, P. Pragacz described the ordinary Hall-Littlewood -polynomials
by means of push-forwards (Gysin maps) from flag bundles in the ordinary
cohomology theory. Together with L. Darondeau, he also gave push-forward
formulas (Gysin formulas) for all flag bundles of types , , and
in the ordinary cohomology theory. In this paper, we introduce a generalization
of the ordinary Hall-Littlewood - and -polynomials, which we call the
{\it universal factorial Hall-Littlewood - and -functions}, and
characterize them in terms of Gysin maps from flag bundles in the complex
cobordism theory. We also generalize the (type ) push-forward formula due to
Darondeau-Pragacz to the complex cobordism theory. As an application of our
Gysin formulas in complex cobordism, we give generating functions for the
universal Hall-Littlewood - and -functions and their factorial analogues.
Using our generating functions, classical determinantal and Pfaffian formulas
for Schur - and -polynomials, and their -theoretic or factorial
analogues can be obtained in a simple and unified manner.Comment: 46 pages, AMSLaTeX; Section 6 added, An error of the generating
function for the universal factorial Hall-Littlewood -functions was
correcte
Excited Young diagrams and equivariant Schubert calculus
We describe the torus-equivariant cohomology ring of isotropic Grassmannians
by using a localization map to the torus fixed points. We present two types of
formulas for equivariant Schubert classes of these homogeneous spaces. The
first formula involves combinatorial objects which we call ``excited Young
diagrams'' and the second one is written in terms of factorial Schur - or
-functions. As an application, we give a Giambelli-type formula for the
equivariant Schubert classes. We also give combinatorial and Pfaffian formulas
for the multiplicity of a singular point in a Schubert variety.Comment: 29 page
Double Schubert polynomials of classical type and Excited Young diagrams (New Trends in Combinatorial Representation Theory)
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