30 citations · 416 across the 73 of their papers we have counts for
7 papers · 1 filter
A panorama of positivity
Alexander Belton, Dominique Guillot, Apoorva Khare +1
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (g…
The non-compact normed space of norms on a finite-dimensional Banach space
Apoorva Khare
We discuss a new pseudometric on the space of all norms on a finite-dimensional vector space (or free module) , with the real, complex, or quaternion num…
Smooth entrywise positivity preservers, a Horn-Loewner master theorem, and symmetric function identities
Apoorva Khare
A special case of a fundamental result of Loewner and Horn [Trans. Amer. Math. Soc. 1969] says that given an integer , if the entrywise application of a smooth function $…
Generalized nil-Coxeter algebras
Apoorva Khare
Motivated by work of Coxeter (1957), we study a class of algebras associated to Coxeter groups, which we term 'generalized nil-Coxeter algebras'. We construct the first finite-dime…
The critical exponent: a novel graph invariant
Dominique Guillot, Apoorva Khare, Bala Rajaratnam
A surprising result of FitzGerald and Horn (1977) shows that is positive semidefinite (p.s.d.) for every entrywise nonnegative p.s.d. matri…
The Weyl-Kac weight formula
Gurbir Dhillon, Apoorva Khare
We provide the first formulae for the weights of all simple highest weight modules over Kac-Moody algebras. For generic highest weights, we present a formula for the weights of sim…