Equivariant algebraic vector bundles over representations of reductive groups: theory.
Abstract
Let G be a reductive algebraic group and let B be an affine variety with an algebraic action of G. Everything is defined over the field C of complex numbers. Consider the trivial G-vector bundle B x S = S over B where S is a G-module. From the endomorphism ring R of the G-vector bundle S a construction of G-vector bundles over B is given. The bundles constructed this way have the property that when added to S they are isomorphic to F + S for a fixed G-module F. For such a bundle E an invariant rho(E) is defined that lies in a quotient of R. This invariant allows us to distinguish nonisomorphic G-vector bundles. This is applied to the case where B is a G-module and, in that case, an invariant of the underlying equivariant variety is given too. These constructions and invariants are used to produce families of inequivalent G-vector bundles over G-modules and families of inequivalent G actions on affine spaces for some finite and some connected semisimple groups.
Keywords
Access
No online access links available
Citation
ID:
97349
References
Blockchain Verification
Account:
NFT Contract Address:
0x95644003c57E6F55A65596E3D9Eac6813e3566dA
Article ID:
97349
Unique Identifier:
Network:
Scimatic Chain (ID: 481)
Loading...
Blockchain Readiness Checklist
Authors
Abstract
Journal Name
Year
Title
Creates 1,000,000 NFT tokens for this article
Token Features:
- ERC-1155 Standard NFT
- 1 Million Supply per Article
- Transferable via MetaMask
- Permanent Blockchain Record
Scan with Saymatik Web3.0 Wallet