Quantum Schubert polynomials
نویسندگان
چکیده
منابع مشابه
Quantum Schubert Polynomials
where In is the ideal generated by symmetric polynomials in x1, . . . , xn without constant term. Another, geometric, description of the cohomology ring of the flag manifold is based on the decomposition of Fln into Schubert cells. These are even-dimensional cells indexed by the elements w of the symmetric group Sn . The corresponding cohomology classes σw , called Schubert classes, form an add...
متن کاملQuantum Schubert Polynomials Sergey
where In is the ideal generated by symmetric polynomials in x1, . . . , xn without constant term. Another, geometric, description of the cohomology ring of the flag manifold is based on the decomposition of Fln into Schubert cells. These are even-dimensional cells indexed by the elements w of the symmetric group Sn . The corresponding cohomology classes σw , called Schubert classes, form an add...
متن کاملEquivariant Quantum Schubert Polynomials
We establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the presentation of the equivariant quantum cohomology ring, as well as Graham-positivity of the structure constants in equivariant quantum Schubert calculus.
متن کاملQuantum double Schubert polynomials, quantum Schubert polynomials and Vafa-Intriligator formula
We study the algebraic aspects of equivariant quantum cohomology algebra of the flag manifold. We introduce and study the quantum double Schubert polynomials S̃w(x, y), which are the Lascoux– Schützenberger type representatives of the equivariant quantum cohomology classes. Our approach is based on the quantum Cauchy identity. We define also quantum Schubert polynomials S̃w(x) as the Gram–Schmidt...
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The quantum Bruhat graph, which is an extension of the graph formed by covering relations in the Bruhat order, is naturally related to the quantum cohomology ring of G/B. We enhance a result of Fulton and Woodward by showing that the minimal monomial in the quantum parameters that occurs in the quantum product of two Schubert classes has a simple interpretation in terms of directed paths in thi...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 1997
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-97-00237-3