Modified Macdonald polynomials and integrability

Alexandr Garbali; Michael Wheeler

Modified Macdonald polynomials and integrability

Combinatorics 2019-11-14 v2 Mathematical Physics math.MP Quantum Algebra

Authors: Alexandr Garbali , Michael Wheeler

Abstract

We derive combinatorial formulae for the modified Macdonald polynomial $H_{\lambda}(x;q,t)$ using coloured paths on a square lattice with quasi-cylindrical boundary conditions. The derivation is based on an integrable model associated to the quantum group of $U_{q}(\wide{sl}_{n+1})$ .

Keywords

macdonald polynomials q-series and q-analogues kazhdan-lusztig polynomials

Cite

@article{arxiv.1810.12905,
  title  = {Modified Macdonald polynomials and integrability},
  author = {Alexandr Garbali and Michael Wheeler},
  journal= {arXiv preprint arXiv:1810.12905},
  year   = {2019}
}

Comments

References corrected, explanations and examples added

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