W algebras and integrable structures

https://hu-berlin.zoom.us/j/61339297016

I will review basic properties of W-algebras, in particular the WN family and the associated Winfinity algebra. These algebraic structures show up at many places in mathematical physics. Winfinity admits two different descriptions: the traditional description starts from the Virasoro algebra of 2d conformal field theory and extends it by local conserved currents of higher spin. The description discovered more recently is the Yangian description manifesting the integrable structure of the algebra. The map between these two pictures is non-trivial, but can be understood by using the Maulik-Okounkov 'instanton' R-matrix as a bridge between these two pictures.