@article{39ad2c73fdfc4e36beb0d339c130ad14,

title = "Semisimplification of the category of tilting modules for GLn",

abstract = "We describe the semisimplification of the monoidal category of tilting modules for the algebraic group GLn in characteristic p>0. In particular, we compute the dimensions of the indecomposable tilting modules modulo p.",

keywords = "Semisimplification, Tensor category, Tilting modules",

author = "Jonathan Brundan and Inna Entova-Aizenbud and Pavel Etingof and Victor Ostrik",

note = "Funding Information: The first author would like to thank Travis Scrimshaw for suggesting the connection to extremal weight crystals, and Ben Elias for many helpful discussions about web categories. The work of V. O. was partially supported by the HSE University Basic Research Program, Russian Academic Excellence Project {\textquoteleft} 5-100 {\textquoteright} and by the NSF grant DMS-1702251 . The work of P. E. was partially supported by the NSF grant DMS-1502244 . Funding Information: This material is based on work supported by The National Science Foundation under Grant No. DMS-1440140 while two of the authors (P.E. and V.O.) were in residence at the Mathematical Sciences Research Institute in Berkeley, California in Spring 2020. The work of J.B. was supported by NSF grant DMS-1700905. The work of I.E. was supported by the ISF grant 711/18. The work of P.E. was also partially supported by the NSF grant DMS-1502244. The work of V.O. was also partially supported by the NSF grant DMS-1702251 and the Russian Academic Excellence Project 5-100.The first author would like to thank Travis Scrimshaw for suggesting the connection to extremal weight crystals, and Ben Elias for many helpful discussions about web categories. The work of V. O. was partially supported by the HSE University Basic Research Program, Russian Academic Excellence Project ?5-100? and by the NSF grant DMS-1702251. The work of P. E. was partially supported by the NSF grant DMS-1502244. Funding Information: This material is based on work supported by The National Science Foundation under Grant No. DMS-1440140 while two of the authors (P.E. and V.O.) were in residence at the Mathematical Sciences Research Institute in Berkeley, California in Spring 2020. The work of J.B. was supported by NSF grant DMS-1700905 . The work of I.E. was supported by the ISF grant 711/18 . The work of P.E. was also partially supported by the NSF grant DMS-1502244 . The work of V.O. was also partially supported by the NSF grant DMS-1702251 and the Russian Academic Excellence Project 5-100 . Publisher Copyright: {\textcopyright} 2020",

year = "2020",

month = dec,

day = "2",

doi = "10.1016/j.aim.2020.107331",

language = "English",

volume = "375",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}