v 1 1 7 O ct 1 99 6 Quantum Schubert polynomials and the Vafa – Intriligator formula
نویسندگان
چکیده
We introduce a quantization map and study the quantization of Schubert and Grothendieck polynomials, monomials, elementary and complete polynomials. Our construction is based on the quantum Cauchy identity. As a corollary, we prove the Lascoux–Schützenberger type formula for quantum Schubert polynomials of the flag manifold. Our formula gives a simple method for computation of quantum Schubert polynomials. We also prove the higher genus analog of Vafa–Intriligator’s formula for the flag manifold. We introduce the Extended Ehresman–Bruhat order on the symmetric group and prove the equivariant quantum Pieri formula. On leave from Steklov Mathematical Institute, Fontanka 27, St.Petersburg, 191011, Russia Supported by JSPS Research Fellowships for Young Scientists
منابع مشابه
Quantum 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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