A plactic algebra of extremal weight crystals and the Cauchy identity
for Schur operators
A plactic algebra of extremal weight crystals and the Cauchy identity
for Schur operators
We give a new bijective interpretation of the Cauchy identity for Schur operators which is a commutation relation between two formal power series with operator coefficients. We introduce a plactic algebra associated with the Kashiwara's extremal weight crystals over the Kac-Moody algebra of type $A_{+\infty}$, and construct a Knuth type …