Hochschild cohomology of generalised Grassmannians
- We compute the Hochschild–Kostant–Rosenberg decomposition of the Hochschild cohomology of generalised Grassmannians, i.e., partial flag varieties associated to maximal parabolic subgroups in a simple algebraic group, in terms of representation-theoretic data.We explain how the decomposition is concentrated in global sections for the (co)minuscule and (co)adjoint generalised Grassmannians, and conjecture that for (almost) all other cases the same vanishing of the higher cohomology does not hold. Our methods give an explicit partial description of the Gerstenhaber algebra structure for the Hochschild cohomology of cominuscule and adjoint generalised Grassmannians. We also consider the case of adjoint partial flag varieties in type A, which are associated to certain submaximal parabolic subgroups.
Download full text files
Statistics
Print On Demand
Additional Services
| Author: | Pieter Belmans, Maxim SmirnovORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1083214 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/108321 |
| ISSN: | 1431-0635OPAC |
| ISSN: | 1431-0643OPAC |
| Parent Title (Uncoded Languages): | Documenta Mathematica |
| Publisher: | European Mathematical Society - EMS - Publishing House |
| Type: | Article |
| Language: | English |
| Date of first Publication: | 2023/08/07 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/10/13 |
| Tag: | General Mathematics |
| Volume: | 28 |
| Issue: | 1 |
| First Page: | 11 |
| Last Page: | 53 |
| DOI: | https://doi.org/10.4171/dm/912 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Algebra und Zahlentheorie | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
