$W_\infty$ modules and melted crystals of DT and PT

Abstract: $W_\infty$ algebra is a vertex operator algebra extending the Virasoro algebra by fields of spin $3,4,\dots$. It is known to admit a nice class of modules labelled by a triple of partitions. $W_\infty$ is also known to admit an alternative description in terms of the affine Yangian of $gl_1$ admitting a very concrete definition of such modules. As we will see in this talk, utilizing the charge-conjugation automorphism of $W_\infty$ in the language of the affine Yangian leads to a new class of affine Yangian modules with non-diagonalizable action of Cartan generators and striking connection with Pandharipande-Thomas invariants.

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar