Shuffle algebras, lattice paths and Macdonald functions
DOI10.1016/j.aim.2024.109974MaRDI QIDQ6639714
Alexandr Garbali, Ajeeth Gunna
Publication date: 18 November 2024
Published in: Advances in Mathematics (Search for Journal in Brave)
Symmetric functions and generalizations (05E05) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Interacting particle systems in time-dependent statistical mechanics (82C22) Exactly solvable models; Bethe ansatz (82B23) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Yang-Baxter equations (16T25)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bethe subalgebras of \(U_q(\widehat{\mathfrak{gl}}_n)\) via shuffle algebras
- Stochastic higher spin vertex models on the line
- Stochastic \(R\) matrix for \(\operatorname{U}_q(A_n^{(1)})\)
- Refined Cauchy/Littlewood identities and six-vertex model partition functions. II: Proofs and new conjectures
- A new generalisation of Macdonald polynomials
- Schur polynomials and the Yang-Baxter equation
- Equivariant \(K\)-theory of Hilbert schemes via shuffle algebra
- Hall polynomials, inverse Kostka polynomials and puzzles
- On a family of symmetric rational functions
- Calculation of norms of Bethe wave functions
- Drinfeld twists and algebraic Bethe ansatz of the supersymmetric model associated with \(U_q(\mathrm{gl}(m| n))\)
- Trigonometric solutions of triangle equations. Simple Lie superalgebras
- Scalar products of Bethe vectors in the models with \(\mathfrak{gl}(m | n)\) symmetry
- The elliptic Hall algebra and the \(K\)-theory of the Hilbert scheme of \(\mathbb{A}^{2}\)
- Modified Macdonald polynomials and integrability
- Spin \(q\)-Whittaker polynomials and deformed quantum Toda
- Scalar products in generalized models with \(\mathrm{SU}(3)\)-symmetry
- Liouville reflection operator, affine Yangian and Bethe ansatz
- Vertex models for canonical Grothendieck polynomials and their duals
- The Shuffle Algebra Revisited
- Moduli of flags of sheaves and their K-theory
- On factorizingF-matrices in \mathcal {Y}(sl_n) and \mathcal {U}_q(\widehat {sl_n}) spin chains
- Matrix product formula for Macdonald polynomials
- A commutative algebra on degenerate CP1 and Macdonald polynomials
- Resolution of the nested hierarchy for rationalsl(n) models
- Shuffle algebras, lattice paths and the commuting scheme
- Nonsymmetric Macdonald polynomials via integrable vertex models
- Factorized domain wall partition functions in trigonometric vertex models
- Quantum toroidal $\mathfrak{g}{{\mathfrak{l}}_{1}}$ and Bethe ansatz
- Coloured stochastic vertex models and their spectral theory
- Colored fermionic vertex models and symmetric functions
- Commutative subalgebra of a shuffle algebra associated with quantum toroidal \(\mathfrak{gl}_{m|n}\)
This page was built for publication: Shuffle algebras, lattice paths and Macdonald functions
