The Weyl algebra (or Heisenberg-Weyl algebra) is the free algebra with two generators $D$ and $U$ and single relation $DU - U D = 1$. As a consequence of this relation, certain monomials are equal, such as $DU U \, D$ and $U \, DDU$. We characterize all such equalities over a field of characteristic 0, describing them in several ways: operational (by a combinatorial equivalence relation generated by certain moves), computational (through lattice path invariants) and in terms of rook theory. We also enumerate the equivalence classes and several variants thereof and discuss possible extensions to other algebras. Joint work with Tom Roby, Stephan Wagner, Mei Yin; inspired by a question of Richard P. Stanley.
De Karol Penson
De Gérard Duchamp
De Jehanne Dousse
De Markus Reineke
De Maxim Kontsevich
De Arthemy Kiselev
De Toshiki Nakashima
De Joseph Ben Geloun
De Stéphane Dartois
De Yuki Kanakubo
De Yiannis Vlassopoulos
De Mohamed Ouerfelli
De Roberta Anna Iseppi
De Alain Connes
