Card shuffling and the decomposition of tensor products
| dc.creator | Fulman, Jason | |
| dc.date | 2003-07-03 | |
| dc.date.accessioned | 2026-07-07T04:59:24Z | |
| dc.date.available | 2026-07-07T04:59:24Z | |
| dc.description | Let H be a subgroup of a finite group G. We use Markov chains to quantify how large r should be so that the decomposition of the r tensor power of the representation of G on cosets on H behaves (after renormalization) like the regular representation of G. For the case where G is a symmetric group and H a parabolic subgroup, we find that this question is precisely equivalent to the question of how large r should be so that r iterations of a shuffling method randomize the Robinson-Schensted-Knuth shape of a permutation. This equivalence is rather remarkable, if only because the representation theory problem is related to a reversible Markov chain on the set of representations of the symmetric group, whereas the card shuffling problem is related to a nonreversible Markov chain on the symmetric group. The equivalence is also useful, and results on card shuffling can be applied to yield sharp results about the decomposition of tensor powers. | |
| dc.identifier | https://arxiv.org/abs/math/0307053 | |
| dc.identifier | http://arxiv.org/abs/math/0307053 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67972 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.title | Card shuffling and the decomposition of tensor products | |
| dc.type | text |