There And Back Again: A Localization's Tale.

1 March 2016
Sian Fryer

The prime spectrum of a quantum algebra has a finite stratification in terms
of a set of distinguished primes called H-primes, and we can study these
strata by passing to certain nice localizations of the algebra.  H-primes
are now starting to show up in some surprising new areas, including
combinatorics (totally nonnegative matrices) and physics, and we can borrow
techniques from these areas to answer questions about quantum algebras and
their localizations.    In particular, we can use Grassmann necklaces -- a
purely combinatorial construction -- to study the topological structure of
the prime spectrum of quantum matrices.