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SUMMARY:Quantum Mechanics of bipartite ribbon graphs and Kronecker coeffic
ients
DTSTART;VALUE=DATE-TIME:20210602T083000Z
DTEND;VALUE=DATE-TIME:20210602T094500Z
DTSTAMP;VALUE=DATE-TIME:20230323T170126Z
UID:indico-contribution-5724@indico.ipmu.jp
DESCRIPTION:Speakers: Sanjaye Ramgoolam (QMUL & U. Witwatersrand)\nI descr
ibe a family of algebras $K(n)$\, one for every positive integer n\, relat
ed to the group algebra of the symmetric group $S_n$. These algebras have
a basis labelled by bi-partite ribbon graphs with $n$ edges. They also hav
e a decomposition into matrix blocks labelled by triples of Young diagram
s with $n$ boxes\, with matrix block size equal to the Kronecker coefficie
nt $C$ for the triple. This leads to algorithms for the determination of
sub-lattices in the lattice of ribbon graphs\, of dimensions $C^2$ and $
C$\, equipped with bases constructed from null vectors of integer matrices
. Some of the algorithms are realised in quantum mechanical systems where
the quantum states are bipartite ribbon graphs. Using the known connection
s between bipartite ribbon graphs and Belyi maps\, these quantum systems h
ave an interpretation as models of quantum membranes.\n\nhttps://indico.ip
mu.jp/event/387/contributions/5724/
LOCATION:Online
URL:https://indico.ipmu.jp/event/387/contributions/5724/
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