# A DG-extension of the nilHecke algebra and symmetric polynomials in type B

The nilHecke algebra of type A, an object of central importance in higher representation theory, admits a differentially-graded extension due to Naisse and Vaz called the extended nilHecke algebra. This latter algebra forms a matrix algebra over a ring of extended symmetric polynomials -- the invariants of the action of the symmetric group on the tensor product of a polynomial algebra and an exterior algebra. In this talk, we extend this work to type B. We will describe a differentially-graded type B extended nilHecke algebra and show that it forms a matrix algebra over a ring of type B extended symmetric polynomials. We will also prove an extended type B analogue of a classical theorem of Solomon which links generating sets of the extended symmetric polynomials to familiar generating sets of the usual symmetric polynomials.