• Corpus ID: 244709774

Complexity of the usual torus action on Kazhdan-Lusztig varieties

  title={Complexity of the usual torus action on Kazhdan-Lusztig varieties},
  author={Maria Donten-Bury and Laura Escobar and Irem Portakal},
We investigate the class of Kazhdan-Lusztig varieties, and its subclass of matrix Schubert varieties, endowed with a naturally defined torus action. Writing a matrix Schubert variety Xw as Xw = Yw × C (where d is maximal possible), we show that Yw can be of complexity-k exactly when k 6= 1. Also, we give a combinatorial description of the extremal rays of the weight cone of a Kazhdan-Lusztig variety, which in particular turns out to be the edge cone of an acyclic directed graph. Finally, we use… 

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