Abstract: In his wonderful paper “Remarks on classical invariant theory”, Roger Howe suggested that his classical duality should be extendable to superalgebras/ supergroups. Roughly speaking, by restricting the spinor-oscillator representation (w, H) of the complex orthosymplectic Lie superalgebra spo(V) to some particular super dual pairs (g, g’) (or (G, g’)), he proved that the action of g’ on every G-isotypic components is irreducible. Some results have been obtained for other dual pairs (Howe, Nishiyama, Sergeev, Cheng-Wang, Howe-Lu, Davidson-Kujawa-Muth ...) but a general theory for a real or complex orthosymplectic Lie superalgebra (or supergroup) is not known yet.
In a recent work with Hadi Salmasian, we obtained a classification of irreducible reductive dual pairs in a real or complex orthosymplectic Lie supergroup SpO(V). Moreover, we proved a “double commutant theorem” for all dual pairs in a real or complex orthosymplectic Lie supergroup.
Time permitting, I will explain other questions we are currently working on related to the extension of Howe duality to super dual pairs.
Bei Interesse an einer online-Teilnahme den Teilnahmelink bitte bei Tobias Weich erfragen.