781 research outputs found
Quantum Integrability and Generalised Quantum Schubert Calculus
We introduce and study a new mathematical structure in the generalised
(quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert
calculus to a quantum integrable system known in the physics literature as the
asymmetric six-vertex model. Our approach offers a new perspective on already
established and well-studied special cases, for example equivariant K-theory,
and in addition allows us to formulate a conjecture on the so-far unknown case
of quantum equivariant K-theory.Comment: 57 pages, 10 figures; v2: some references added and some minor
changes; v3: abstract shortened, some typos corrected and a discussion of the
Bethe roots for the non-equivariant case added; v4: accepted versio
Grothendieck polynomials and the Boson-Fermion correspondence
In this paper we study algebraic and combinatorial properties of Grothendieck
polynomials and their dual polynomials by means of the Boson-Fermion
correspondence. We show that these symmetric functions can be expressed as a
vacuum expectation value of some operator that is written in terms of
free-fermions. By using the free-fermionic expressions, we obtain alternative
proofs of determinantal formulas and Pieri type formulas.Comment: 19 page
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