Note on Laplace operators and homologies of a few Lie subalgebras of $A_1^{(1)}$
| dc.creator | Weinstein, F. V. | |
| dc.date | 2006-04-28 | |
| dc.date | 2006-05-12 | |
| dc.date.accessioned | 2026-07-07T07:11:22Z | |
| dc.date.available | 2026-07-07T07:11:22Z | |
| dc.description | We investigate a spectrum of positive self-adjoint operator $\Gk$ (Laplace operator) acting in the external complexes of some interesting subalgebras $\Lk$ of Lie algebra $A_1^{(1)}$. We obtain an explicit formula for the action of $\G_k$. This formula is used to compute the homology of $\Lk$ with trivial coefficients for $k=-1,0,1,2$. In these cases we show that a spectrum of $\G_k$ is the set of non-negative integers with a finite multiplicity of each eigenvalue for $k=-1,0$, infinite one for $k=1,2$. We also found the generating functions for the multiplicities of $\G_k$-eigenvalues (in appropriate sense for $\G_1$ and $\G_2$). | |
| dc.identifier | https://arxiv.org/abs/math/0604632 | |
| dc.identifier | http://arxiv.org/abs/math/0604632 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111730 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 17B68 | |
| dc.title | Note on Laplace operators and homologies of a few Lie subalgebras of $A_1^{(1)}$ | |
| dc.type | text |