# Chiralization of cluster structures

### APA

Bershtein, M. (2024). Chiralization of cluster structures. Perimeter Institute. https://pirsa.org/24100117

### MLA

Bershtein, Mikhail. Chiralization of cluster structures. Perimeter Institute, Oct. 17, 2024, https://pirsa.org/24100117

### BibTex

@misc{ pirsa_PIRSA:24100117, doi = {10.48660/24100117}, url = {https://pirsa.org/24100117}, author = {Bershtein, Mikhail}, keywords = {Mathematical physics}, language = {en}, title = {Chiralization of cluster structures}, publisher = {Perimeter Institute}, year = {2024}, month = {oct}, note = {PIRSA:24100117 see, \url{https://pirsa.org}} }

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Abstract

The chiralization in the title denotes a certain procedure which turns cluster X-varieties into q-W algebras. Many important notions from cluster and q-W worlds, such as mutations, global functions, screening operators, R-matrices, etc emerge naturally in this context. In particular, we discover new bosonizations of q-W algebras and establish connections between previously known bosonizations. If time permits, I will discuss potential applications of our approach to the study of 3d topological theories and local systems with affine gauge groups.
Based on a joint project with J. Shiraishi, J.E. Bourgine, B. Feigin, A. Shapiro, and G. Schrader.