David Hernandez

Publications, preprints :

[63] Representations and characters of quantum affine algebras at the crossroads between cluster categorification and quantum integrable models : PDF , to appear in Proceedings of the ICM 2026 .

[62] Cluster algebras and shifted quantum groups , PDF , à paraître dans Oberwolfach Reports.

[62] Cluster algebras and shifted quantum groups : PDF , to appear in Oberwolfach Reports.

[61] Extremal monomial property of q-characters and polynomiality of the X-series (with E. Frenkel) : PDF, Chari’s volume of Journal of Algebraic Combinatorics 62 (2025), no. 41.

[60] Jordan-Hölder property for shifted quantum affine algebras (with H. Zhang) : PDF, Preprint arXiv:2501.16859.

[59] Symmetries of Grothendieck rings in representation theory , PDF, to appear in Proceedings of the ECM 2024 : 9th European Congress of Mathematics.

[58] Introduction to Galois Theory (with Y. Laszlo), book, Springer Undergraduate Mathematics Series (2024).

[57] Monoidal Jantzen filtrations (with R. Fujita) : PDF, Preprint arXiv:2402.13544.

[56] Representations of shifted quantum affine algebras and cluster algebras I. The simply-laced case (with C. Geiss and B. Leclerc) : PDF, Proceedings of the London Mathematical Society 129 (2024), no. 3, e12630.

[55] Extended Baxter relations and QQ-systems for quantum affine algebras (with E. Frenkel) : PDF, Communications in Mathematical Physics 405 (2024), 190.

[54] Isomorphisms among quantum Grothendieck rings and cluster algebras (with R. Fujita, S-J. Oh and H. Oya) : PDF, Preprint arXiv:2304.02562.

[53] Weyl group symmetry of q-characters (with E. Frenkel) : PDF , Selecta Mathematica 31 (2025), no. 72.

[52] Representations of shifted quantum groups (or quantized Coulomb branches) and Baxter polynomials : PDF , in Oberwolfach Reports 18 (2021), 2827--2891.

[51] 3-facets of R-matrices: stable maps, intertwiners and transfer-matrices : PDF , in Oberwolfach Reports 18 (2021), 2791--2825.

[50] Folded quantum integrable models and deformed W-algebras (with E. Frenkel and N. Reshetikhin) : PDF , Letters in Mathematical Physics 112 (2022), no. 4, 80.

[49] Langlands duality, shifted quantum groups and cluster algebras : PDF , in Oberwolfach Reports 18 (2021), 1087--1148..

[48] Shifted Yangians and polynomial R-matrices (with H. Zhang) : PDF , Publications of the Research Institute for Mathematical Sciences 60 (2024), no. 1, 1--69.

[47] Isomorphisms among quantum Grothendieck rings and propagation of positivity (with R. Fujita, S-J. Oh and H. Oya) : PDF , Crelle - Journal für die reine und angewandte Mathematik 785 (2022), 117--185.

[46] Representations of shifted quantum affine algebras : PDF , International Mathematical Research Notices (2023), no. 13, 11035–11126..

[45] Toroidal Grothendieck rings and cluster algebras (avec L. Fedele) : PDF , Mathematische Zeitschrift 300 (2022), no. 1, 377--420..

[44] Quantum periodicity and Kirillov-Reshetikhin modules : PDF , in Progress in Mathematics 340 (2021), vol. in Honor of N. Reshetikhin.

[43] Stable maps, Q-operators and category O : PDF, Representation Theory 26 (2022), 179--210.

[42] Quantum affine algebras and cluster algebras (with B. Leclerc) : PDF, in Progress in Mathematics 337 (2021), vol. in Honor of V. Chari.

[41] Grothendieck ring isomorphims, cluster algebras and Kazhdan-Lusztig polynomials : PDF , in Oberwolfach Reports 15 (2018), 3081--3146 .

[40] Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm (with H. Oya) : PDF , Advances in Mathematics 347 (2019), 192--272 .

[39] Cyclicity and R-matrices : PDF , Selecta Mathematica (N.S.) 25 (2019), no.2, 25:19..

[38] Spectra of quantum integrable systems and cluster algebras, Langlands duality and category O : PDF , in Oberwolfach Reports 14 (2017), 1281--1347 .

[37] Advances in R-matrices and their applications (after Maulik-Okounkov, Kang-Kashiwara-Kim-Oh,...) : PDF (translation) , Sém. Bourbaki 1129, Astérisque 407 (2019), 297--331.

[36] Spectra of quantum KdV Hamiltonians, Langlands duality, and affine opers (with E. Frenkel) : PDF , Communications in Mathematical Physics 362 (2018), no. 2, 361--414.

[35] Cluster algebras and category O for representations of Borel subalgebras of quantum affine algebras (with B. Leclerc) : PDF , Algebra and Number Theory 10 (2016), no. 9, 2015--2052.

[34] Asymptotical representations, spectra of quantum integrable systems and cluster algebras : PDF , in Oberwolfach Reports 12 (2015), 1385--1447.

[33] Polynômes, représentations et systèmes quantiques : PDF , Images des Mathématiques, CNRS (2014).

[32] Spectre des systèmes intégrables quantiques représentations linéaires : PDF , Gazette des Mathématiciens 141 (2014), 34--47.

[31] Schur positivity and Kirillov-Reshetikhin modules (with G. Fourier) : PDF , Special issue of SIGMA "New Directions in Lie Theory" 10 (2014), 058

[30] Baxter's Relations and Spectra of Quantum Integrable Models (with E. Frenkel) : PDF , Duke Mathematical Journal 164 (2015), no. 12, 2407--2460.

[29] A cluster algebra approach to q-characters of Kirillov-Reshetikhin modules (with B. Leclerc) : PDF , Journal of the European Mathematical Society 18 (2016), no. 5, 1113--1159

[28] Monoidal categorifications of cluster algebras of type A and D (with B. Leclerc) : PDF , in Symmetries, Integrable systems and Representations, Springer Proceedings in Mathematics and Statistics 40 (2013), 175--193

[27] Quantum Grothendieck rings and derived Hall algebras (with B. Leclerc) : PDF ,Crelle - Journal für die reine und angewandte Mathematik 701 (2015), 77--126

[26] Asymptotic representations and Drinfeld rational fractions (with M. Jimbo) : PDF , Compositio Mathematica 148 (2012), no. 5, 1593--1623

[25] Introduction à la théorie de Galois (with Y. Laszlo) : Book, Editions de l'Ecole polytechnique (2012)

[24] Simple tensor products of representations of quantum affine algebras : PDF , in Oberwolfach Reports 7 (2010), no. 1, 799--882

[23] The algebra $U_q(\hat{sl}_\infty)$ and applications : PDF , De Concini's issue of Journal of Algebra 329 (2011), no. 1, 147--162

[22] Simple tensor products : PDF , Inventiones Mathematicae 181 (2010), no. 3, 649--675

[21] Autour des représentations des algèbres quantiques : géométrie, dualité de Langlands et catégorification des algèbres cluster : PDF , Habilitation à diriger des recherches Université Paris VII (2009)

[20] Cluster algebras and quantum affine algebras (with B. Leclerc) : PDF , Duke Mathematical Journal 154 (2010), no. 2, 265--341

[19] Langlands duality for finite-dimensional representations of quantum affine algebras (with E. Frenkel) : PDF , Letters in Mathematical Physics 96 (2011), no. 1-3, 217--261

[18] Double affine Lie algebras and finite groups (with N. Guay and S. Loktev) : PDF , Pacific Journal of Mathematics 243 (2009), no. 1, 1--41

[17] Geometry of the analytic loop group (with C. De Concini and N. Reshetikhin) : PDF , Advances in Mathematics 238 (2013), 290--321

[16] Beyond Kirillov-Reshetikhin modules (with V. Chari) : PDF , Contemporary Mathematics 506 (2010), 49--81

[15] Langlands duality for representations of quantum groups (with E. Frenkel) : PDF , Mathematische Annalen 349 (2011), no. 3, 705--746

[14] Quantum toroidal algebras and their representations : PDF , Selecta Mathematica (N.S.) 14 (2009), no. 3-4, 701--725

[13] Kirillov-Reshetikhin conjecture : the general case : PDF, International Mathematics Research Notices 2010, no. 1, 149--193

[12] On minimal affinizations of representations of quantum groups : PDF , Communications in Mathematical Physics 277 (2007), no. 1, 221--259

[11] Smallness problem for quantum affine algebras and quiver varieties : PDF , Annales Scientifiques de l'Ecole Normale Supérieure (4) 41 (2008) , no. 2, 271-306

[10] Level 0 monomial crystals (with H. Nakajima) : PDF , Lusztig's issue of Nagoya Mathematical Journal 184 (2006), 85--153

[9] Drinfeld coproduct, quantum fusion tensor category and applications : PDF , Proceedings of the London Mathematical Society (3) 95 (2007), no. 3, 567--608

[8] An Introduction to Affine Kac-Moody Algebras : PDF , Ctqm Master Class Series 2 (2006), 1--20

[7] The Kirillov-Reshetikhin conjecture and solutions of T-systems : PDF , Crelle - Journal für die reine und angewandte Mathematik 596 (2006), 63--87

[6] Représentations des algèbres affinisées quantiques : q,t-caractères et produit de fusion. : PDF , Ph.D thesis Université Paris VI (2004)

[5] Monomials of q and q,t-characters for non simply-laced quantum affinizations : PDF , Mathematische Zeitschrift 250 (2005), no. 2, 443--473

[4] Representations of Quantum Affinizations and Fusion Product : PDF , Transformation Groups 10 (2005), no. 2, 163--200

[3] The t-Analogs of q-Characters at Roots of Unity for Quantum Affine Algebras and Beyond : PDF , Journal of Algebra 279 (2004), no. 2 , 514--557

[2] Algebraic Approach to q,t-Characters : PDF , Advances in Mathematics 187 (2004), no. 1, 1--52

[1] t-analogues des opérateurs d'écrantage associés aux q-caractères : PDF , International Mathematics Research Notices 2003, no. 8, 451--475