Loïc Poulain d'Andecy

Summary

Position: Maître de Conférences, Université de Reims Champagne Ardenne

Research team: Groupes et Quantification, Laboratoire de Mathématiques de Reims (LMR), CNRS, FRE 2011

Research keywords: Representation Theory; Mathematical Physics; Knots and links; Lie Algebras and Quantum Groups; Hecke Algebras; Braid Group; Integrable systems; Yang-Baxter Equation; Orthogonal Polynomials

Curriculum Vitae : here

ANR Project Young Researcher 2019 - 2023

Agence Nationale de la Recherche, JCJC Project ANR-18-CE40-0001

• Title: "Applications of Hecke Algebras: Representations, Knots and Physics"
• Acronym: AHA
• Coordinator: Loïc Poulain d'Andecy
• Webpage: here

International Research project (IRP) 2021 - 2026

jointly supported by INSMI & INP,

• Title: "Approches Algébriques de la Physique Théorique"
• Acronym: AAPT
• Coordinator: Nicolas Crampé
• Webpage: see here

Events

• 16th - 21st July 2023: Final conference of the ANR project AHA, "Hecke algebras and applications", Spetses.
• February 27th - 3rd March 2023: Winter school of the ANR project AHA, "Applications of Hecke and related algebras: Representations, Integrability and Physics", Les Houches.
• 23th May - 10th June 2022: Non-commutative algebras, representation theory and special functions , in the thematic semester Symmetries: Algebras and Physics Montreal.
• 4th - 7th March 2019: Winter Braids IX , Reims.
• 14 - 15 février 2019 : Réunion de lancement du projet ANR AHA , Reims.
• 21st - 22nd June 2018 : Journées de Combinatoire Algébrique , Champinatoire II , Reims.
• 2nd - 3rd June 2016 : Journées du GDR TLAG , Théorie de Lie Algébrique et Géométrique , Reims.

Publications

• On ArXiv

HDR thesis

Centralisers and Hecke algebras in Representation Theory, with applications to Knots and Physics

Papers

1. (with A. Lacabanne) Framization of Schur-Weyl duality and Yokonuma-Hecke type algebras, preprint arXiv:2312.14796
2. (with N. Crampé, J. Gaboriaud and L. Vinet) Matrix elements of SO(3) in sl_3 representations as bispectral multivariate functions, Journal of Mathematical Physics 64 (2023), no. 11, Paper No. 111702, 16pp.
3. (with M. Zaimi) Fused Hecke algebra and one-boundary algebras, to appear in Pacific Journal of Mathematics arXiv:2306.10937
4. (with Q. Labriet) Identities for Rankin-Cohen brackets, Racah coefficients and associativity, to appear in Letters in Mathematical Physics arXiv:2304.10803
5. (with Q. Labriet) Realisations of Racah algebras using Jacobi operators and convolution identities, Advances in Applied Mathematics 153 (2024), Paper No. 102620, 31pp.
6. (with N. Crampé, L. Frappat and E. Ragoucy) The higher-rank Askey--Wilson algebra and its braid group automorphisms, SIGMA Symmetry Integrability and Geometry. Methods and Applications 19 (2023) Paper No. 077, 36pp.
7. (with P.-A. Bernard, N. Crampé, L. Vinet and M. Zaimi) Bivariate P-polynomial association schemes, to appear in Algebraic Combinatorics arXiv:2212.10824
8. (with N. Crampé, L. Vinet and M. Zaimi) Askey-Wilson braid algebra and centralizer of U_q(sl_2), Annales de l'Institut Henri Poincaré 24 (2023), no. 6, 1897-1922.
9. (with P.-A. Bernard, N. Crampé, R. Nepomechie, G. Parez and L. Vinet) Entanglement of inhomogeneous free fermions on hyperplane lattices, Nuclear Physics B 984 (2022) Paper No.115975, 28pp.
10. Fusion for the Yang-Baxter equation and the braid group, Winter Braids Lecture Notes Vol. 7 (2020), Course III, p. 1-49.
11. (with N. Crampé and L. Vinet) The missing label of su_3 and its symmetry, Communications in Mathematical Physics 400 (2023), no. 1, 179-213.
12. (with N. Crampé, J. Gaboriaud and L. Vinet) Racah algebras, the centralizer Z_n(sl_2) and its Hilbert-Poincaré series, Annales de l'Institut Henri Poincaré 23 (2022), no. 7, 2657-2682.
13. (with N. Crampé, L. Frappat, J. Gaboriaud, E. Ragoucy and L. Vinet) The Askey-Wilson algebra and its avatars, Journal of Physics A: Mathematical and Theoretical 54 (2021) no. 6, 063001 (32pp).
14. (with N. Crampé and L. Vinet) A Calabi-Yau algebra with E6 symmetry and the Clebsch-Gordan series of sl(3), Journal of Lie Theory 31 (2021), no. 4, 1085-1112.
15. (with N. Crampé) Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry, Letters in Mathematical Physics 111 (2021), no. 4, Paper No. 92, 21 pp.
16. (with N. Crampé) Fused braids and centralisers of tensor representations of Uq(glN), Algebras and Representation Theory 26 (2023), no. 3, 901-955
17. (with N. Crampé and L. Vinet) Temperley-Lieb, Brauer and Racah algebras and other centralizers of su(2), Transactions of the American Mathematical Society 373 (2020), no. 7, 4907-4932.
18. (with S. Rostam) Morita equivalences for cyclotomic Hecke algebras of type B and D, Bulletin de la Société Mathématique de France 149 (2021), no. 1, 179-233.
19. (with R. Walker) Affine Hecke algebras of type D and generalisations of quiver Hecke algebras, Journal of Algebra 552 (2020), 1-37.
20. (with R. Walker) Affine Hecke algebras and generalisations of quiver Hecke algebras for type B, Proceedings of the Edinburgh Mathematical Society 63(2) (2020) 531-578.
21. (with A.-L. Thiel and E. Wagner) Inductive basis on Birman-Murakami-Wenzl algebras and (transverse) Markov traces, preprint .
22. (with N. Jacon) Clifford theory for Yokonuma--Hecke algebras and deformation of complex reflection groups, Journal of the London Mathematical Society (2) 96 (2017), no. 3, 501-523.
23. (with E. Wagner) The HOMFLYPT polynomials of sublinks and the Yokonuma-Hecke algebras, Proceedings of the Royal Society of Edinburgh, Section A 148 (2018), no. 6, 1269-1278.
24. Young tableaux and representations of Hecke algebras of type ADE, Journal of Combinatorial Algebra 1 (2017), 371-423.
25. Invariants for links from classical and affine Yokonuma--Hecke algebras, "Algebraic Modeling of Topological and Computational Structures and Applications", Springer Proceedings in Mathematics & Statistics 219 (2017) 77-95.
26. (with N. Jacon) An isomorphism theorem for Yokonuma--Hecke algebras and applications to link invariants, Mathematische Zeitschrift 283 (2016), no. 1, 301-338.
27. (with M. Chlouveraki) Markov traces on cyclotomic and affine Yokonuma--Hecke algebras, International Mathematics Research Notices (2016), no.14, 4167–4228.
28. (with O. Ogievetsky) Induced representations and traces for chains of affine and cyclotomic Hecke algebras, Journal of Geometry and Physics 87 (2015), 354-372.
29. Fusion formulas and fusion procedure for the Yang--Baxter equation, Algebras and Representation Theory 20 (2017), no. 6, 1379-1414.
30. (with M. Chlouveraki) Representation theory of the Yokonuma--Hecke algebra, Advances in Mathematics 259 (2014), no. 10, 134-172.
31. Fusion procedure for wreath products of finite groups by the symmetric group, Algebras and Representation Theory 17 (2014), no. 3, 809-830.
32. (with O. Ogievetsky) Fusion procedure for cyclotomic Hecke algebras, SIGMA Symmetry Integrability and Geometry. Methods and Applications 10 (2014), 039, 13 pages.
33. (with O. Ogievetsky) Alternating subalgebras of Hecke algebras and alternating subgroups of braid groups, Communications in Algebra 42 (2014), no. 5, 1921-1936.
34. (with O. Ogievetsky) Jucys--Murphy elements and representations of cyclotomic Hecke algebras, preprint.
35. (with O. Ogievetsky) On representations of complex reflection groups G(m,1,n), Theoretical and Mathematical Physics 174 (2013), no. 1, 95-108.
36. (with O. Ogievetsky) Alternating subgroups of Coxeter groups and their spinor extensions, Journal of Pure and Applied Algebra 217 (2013), no. 11, 2198-2211.
37. (with O. Ogievetsky) Fusion procedure for Coxeter groups of type B and complex reflection groups G(m,1,n), Proceedings of the AMS 142 (2014), no. 9, 2929-2941.
38. (with O. Ogievetsky) On representations of cyclotomic Hecke algebras, Modern Physics Letters A 26 (2011), no. 11, 795-803.