| Autor: |
Martin Rubey, Bruce W. Westbury |
| Jazyk: |
angličtina |
| Rok vydání: |
2015 |
| Předmět: |
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| Zdroj: |
Discrete Mathematics & Theoretical Computer Science, Vol DMTCS Proceedings, 27th..., Iss Proceedings (2015) |
| Druh dokumentu: |
article |
| ISSN: |
1365-8050 |
| DOI: |
10.46298/dmtcs.2508 |
| Popis: |
An important problem from invariant theory is to describe the subspace of a tensor power of a representation invariant under the action of the group. According to Weyl's classic, the first main (later: 'fundamental') theorem of invariant theory states that all invariants are expressible in terms of a finite number among them, whereas a second main theorem determines the relations between those basic invariants.Here we present a transparent, combinatorial proof of a second fundamental theorem for the defining representation of the symplectic group $Sp(2n)$. Our formulation is completely explicit and provides a very precise link to $(n+1)$-noncrossing perfect matchings, going beyond a dimension count. As a corollary, we obtain an instance of the cyclic sieving phenomenon. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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