Homotopy transfer and self-dual Schur modules

Michel Dubois-Violette (1) , Todor Popov (2)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]
2 INRNE - Institute for Nuclear Research and Nuclear Energy

We consider the free 2-nilpotent graded Lie algebra g generated in degree one by a finite dimensional vector space V . We recall the beautiful result that the cohomology H*(g,K) of g with trivial coefficients carries a GL(V)-representation having only the Schur modules Vλ with self-dual Young diagrams {λ : λ = λ′} (each with multiplicity one) in its decomposition into GL(V )-irreducibles. The homotopy transfer theorem due to Tornike Kadeishvili allows to equip the cohomology of the Lie algebra g with a structure of homotopy commutative algebra.

Domaines: Physique mathématique [math-ph]

Michel Dubois-Violette, Todor Popov. Homotopy transfer and self-dual Schur modules. Physics of Particles and Nuclei, 2012, 43 (5), pp.708-710. ⟨10.1134/S1063779612050115⟩. ⟨hal-00667215⟩