Seminar

Canonical bases in modules over Lie algebras and quantum groups, Weyl groups and Hecke algebras etc. enjoy a rich plethora of algebraic and combinatorial structures; according to the Kazhdan-Lusztig theory they also contain a lot of information about the categorification of the module. Recent progress in representation theory of quantized symplectic singularities indicates that their cohomology should admit such bases, although understanding their algebraic and combinatorial properties is only beginning to emerge. Already the case of the quotient singularity C^{2n}/S_n leading to new bases in the space of symmetric polynomials leads to several open questions.