Abstract
In classical linear algebra, given a diagonalizable operator on a vector space, Lagrange interpolation produces an idempotent decomposition of the identity corresponding to the projections to eigenspaces. In this chapter, we explain a categorical analogue of this procedure, due to Elias and Hogancamp: given a “diagonalizable” functor acting on a monoidal homotopy category, we produce idempotent functors which project to “eigencategories.” The main application is to the full twist Rouquier complex, acting on the homotopy category of Soergel bimodules.
This chapter is based on expanded notes of a lecture given by the authors and taken by Alex Chandler, Nachiket Karnick, and Dmitry Vagner
A. Chandler Department of Mathematics, North Carolina State University, Raleigh, NC, USA N. Karnick Department of Mathematics, Indiana University-Bloomington, Bloomington, IN, USA D. Vagner Department of Mathematics, Duke University, Durham, NC, USA
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
B. Elias, M. Hogancamp, Categorical Diagonalization (2017). arXiv:1707.04349
B. Elias, M. Hogancamp, Categorical Diagonalization of Full Twists (2017). arXiv:1801.00191
A. Mathas, On the left cell representations of Iwahori-Hecke algebras of finite Coxeter groups. J. Lond. Math. Soc. (2) 54(3), 475–488 (1996). https://doi.org/10.1112/jlms/54.3.475
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Elias, B., Makisumi, S., Thiel, U., Williamson, G. (2020). Categorical Diagonalization. In: Introduction to Soergel Bimodules. RSME Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-48826-0_23
Download citation
DOI: https://doi.org/10.1007/978-3-030-48826-0_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-48825-3
Online ISBN: 978-3-030-48826-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)