Reciprocity Algebras and Branching for Classical Symmetric Pairs
| dc.creator | Howe, Roger E. | |
| dc.creator | Tan, Eng Chye | |
| dc.creator | Willenbring, Jeb F. | |
| dc.date | 2004-07-27 | |
| dc.date | 2005-11-06 | |
| dc.date.accessioned | 2026-07-07T06:38:41Z | |
| dc.date.available | 2026-07-07T06:38:41Z | |
| dc.description | We study branching laws for a classical group $G$ and a symmetric subgroup $H$. Our approach is through the {\it branching algebra}, the algebra of covariants for $H$ in the regular functions on the natural torus bundle over the flag manifold for $G$. We give concrete descriptions of (natural subalgebras of) the branching algebra using classical invariant theory. In this context, it turns out that the ten classes of classical symmetric pairs $(G,H)$ are associated in pairs, $(G,H)$ and $(H',G')$, and that the (partial) branching algebra for $(G,H)$ also describes a branching law from $H'$ to $G'$. (However, the second branching law may involve certain infinite-dimensional highest weight modules for $H'$.) To highlight the fact that these algebras describe two branching laws simultaneously, we call them {\it reciprocity algebras}. Our description of the reciprocity algebras reveals that they all are related to the tensor product algebra for $GL_n$. This relation is especially strong in the {\it stable range}. We give quite explicit descriptions of reciprocity algebras in the stable range in terms of the tensor product algebra for $GL_n$. This is the structure lying behind formulas for branching multiplicities in terms of Littlewood-Richardson coefficients. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/math/0407467 | |
| dc.identifier | http://arxiv.org/abs/math/0407467 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100826 | |
| dc.subject | Representation Theory | |
| dc.title | Reciprocity Algebras and Branching for Classical Symmetric Pairs | |
| dc.type | text |