We study exactly solvable lattice models associated to canonical Grothendieck polynomials and their duals. We derive inversion relations and Cauchy identities.
Revised:
Accepted:
Published online:
Keywords: Grothendieck polynomials, Exactly solvable lattice models
Gunna, Ajeeth 1; Zinn-Justin, Paul 1
@article{ALCO_2023__6_1_109_0, author = {Gunna, Ajeeth and Zinn-Justin, Paul}, title = {Vertex models for {Canonical} {Grothendieck} polynomials and their duals}, journal = {Algebraic Combinatorics}, pages = {109--163}, publisher = {The Combinatorics Consortium}, volume = {6}, number = {1}, year = {2023}, doi = {10.5802/alco.235}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.235/} }
TY - JOUR AU - Gunna, Ajeeth AU - Zinn-Justin, Paul TI - Vertex models for Canonical Grothendieck polynomials and their duals JO - Algebraic Combinatorics PY - 2023 SP - 109 EP - 163 VL - 6 IS - 1 PB - The Combinatorics Consortium UR - https://alco.centre-mersenne.org/articles/10.5802/alco.235/ DO - 10.5802/alco.235 LA - en ID - ALCO_2023__6_1_109_0 ER -
%0 Journal Article %A Gunna, Ajeeth %A Zinn-Justin, Paul %T Vertex models for Canonical Grothendieck polynomials and their duals %J Algebraic Combinatorics %D 2023 %P 109-163 %V 6 %N 1 %I The Combinatorics Consortium %U https://alco.centre-mersenne.org/articles/10.5802/alco.235/ %R 10.5802/alco.235 %G en %F ALCO_2023__6_1_109_0
Gunna, Ajeeth; Zinn-Justin, Paul. Vertex models for Canonical Grothendieck polynomials and their duals. Algebraic Combinatorics, Volume 6 (2023) no. 1, pp. 109-163. doi : 10.5802/alco.235. https://alco.centre-mersenne.org/articles/10.5802/alco.235/
[1] A Littlewood–Richardson rule for the -theory of Grassmannians, Acta Math., Volume 189 (2002) no. 1, pp. 37-78 | DOI | MR | Zbl
[2] Double Grothendieck polynomials and colored lattice models, Int. Math. Res. Not. IMRN (2022) no. 10, pp. 7231-7258 | DOI | MR | Zbl
[3] Yang–Baxter equation, symmetric functions and Grothendieck polynomials, 1993
[4] Young tableaux. With applications to representation theory and geometry, London Mathematical Society Student Texts, 35, Cambridge University Press, Cambridge, 1997, x+260 pages | MR
[5] Modified honeycombs in K-Homology of Grassmannian (work in progress.)
[6] Interacting dimers on the honeycomb lattice: an exact solution of the five-vertex model, Physica A, Volume 228 (1996), pp. 1-32 | DOI | MR
[7] Schubert puzzles and integrability I: invariant trilinear forms, 2017
[8] Combinatorial Hopf algebras and -homology of Grassmannians, Int. Math. Res. Not. IMRN (2007) no. 24, p. Art. ID rnm125, 48 pages | DOI | MR | Zbl
[9] Finite sum Cauchy identity for dual Grothendieck polynomials, Proc. Japan Acad. Ser. A Math. Sci., Volume 90 (2014) no. 7, pp. 87-91 | DOI | MR | Zbl
[10] Symmetry and flag manifolds, Invariant Theory (Gherardelli, Francesco, ed.), Springer Berlin Heidelberg, Berlin, Heidelberg (1983), pp. 118-144 | DOI | Zbl
[11] On the Yang–Baxter equation for the six-vertex model, Nuclear Phys. B, Volume 882 (2014), pp. 70-96 | DOI | MR | Zbl
[12] Factorial Grothendieck polynomials, Electron. J. Combin., Volume 13 (2006) no. 1, p. Research Paper 71, 40 pages | DOI | MR | Zbl
[13] Vertex models, TASEP and Grothendieck polynomials, J. Phys. A, Volume 46 (2013), Paper no. 355201, 26 pages | DOI | MR | Zbl
[14] K-theoretic boson-fermion correspondence and melting crystals, J. Phys. A, Volume 47 (2014), Paper no. 445202, 30 pages | DOI | MR | Zbl
[15] Littlewood–Richardson coefficients for Grothendieck polynomials from integrability, J. Reine Angew. Math., Volume 757 (2019), pp. 159-195 | DOI | MR | Zbl
[16] Duality and deformations of stable Grothendieck polynomials, J. Algebraic Combin., Volume 45 (2017) no. 1, pp. 295-344 | DOI | MR | Zbl
[17] Symmetric Grothendieck polynomials, skew Cauchy identities, and dual filtered Young graphs, J. Comb. Theory, Ser. A, Volume 161 (2019), pp. 453-485 | DOI | MR | Zbl
[18] Enumeration of plane partitions by descents, J. Combin. Theory Ser. A, Volume 178 (2021), Paper no. 105367, 18 pages | DOI | MR | Zbl
[19] Six-vertex, loop and tiling models: integrability and combinatorics, Lambert Academic Publishing, 2009 http://www.lpthe.jussieu.fr/~pzinn/publi/hdr.pdf (Habilitation thesis)
[20] Schur functions and Littlewood–Richardson rule from exactly solvable tiling models, 2012 http://www.lpthe.jussieu.fr/~pzinn/semi/berkeley.pdf (Chern–Simons Research Lectures)
Cited by Sources: