Abstract:We formulate and study the spin nilHecke algebras b NHn and d NHn of type B/D, which differ from the usual nilHecke algebras by some odd signs. The type B spin nilHecke algebra is a nil version of the spin type B Hecke algebra introduced earlier by the second author and Khongsap, but not for the type D one. We construct faithful polynomial representations Poln of the nilHecke algebras via odd Demazure operators. We formulate the spin Schubert polynomials, and use them to show that the spin nilHecke algebras ar… Show more
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