Extremal irreducible modules over quantized Coulomb branches

There is a class of irreducible modules over quantized Coulomb branches of quiver gauge theories known as “extremal” modules. These modules arise naturally both in the representation theory of shifted Yangians and in the enumerative geometry discussed in Tommaso’s talk. I will report on results concerning the characters and q-characters of these modules, as well as the related geometry of Coulomb branches, with an emphasis on what happens beyond finite-type quivers. I will also explain their relationship with “classical” combinatorics and discuss the general “slant-sum” operation on quiver gauge theories that we propose. This talk is based on joint work with Dinkins and Reese, as well as on work in progress with Cai, Klyuev, and Yan.

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