On the natural representation of $S(Ω)$ into $L^2(P(Ω))$: Discrete harmonics and Fourier transform
| dc.creator | Marco, José Manuel | |
| dc.creator | Parcet, Javier | |
| dc.date | 2003-12-11 | |
| dc.date.accessioned | 2026-07-07T05:03:48Z | |
| dc.date.available | 2026-07-07T05:03:48Z | |
| dc.description | Let $Ω$ denote a non-empty finite set. Let $S(Ω)$ stand for the symmetric group on $Ω$ and let us write $P(Ω)$ for the power set of $Ω$. Let $ρ: S(Ω) \to U(L^2(P(Ω)))$ be the left unitary representation of $S(Ω)$ associated with its natural action on $P(Ω)$. We consider the algebra consisting of those endomorphisms of $L^2(P(Ω))$ which commute with the action of $ρ$. We find an attractive basis $B$ for this algebra. We obtain an expression, as a linear combination of $B$, for the product of any two elements of $B$. We obtain an expression, as a linear combination of $B$, for the adjoint of each element of $B$. It turns out the Fourier transform on $P(Ω)$ is an element of our algebra; we give the matrix which represents this transform with respect to $B$. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0312232 | |
| dc.identifier | http://arxiv.org/abs/math/0312232 | |
| dc.identifier | J. Combin. Theory Ser. A 100 (2002), 153-175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69563 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.subject | 05E10; 05E30 | |
| dc.title | On the natural representation of $S(Ω)$ into $L^2(P(Ω))$: Discrete harmonics and Fourier transform | |
| dc.type | text |