30 citations · 416 across the 73 of their papers we have counts for
10 papers · 1 filter
The lattice of nil-Hecke algebras over real and complex reflection groups
Sutanay Bhattacharya, Apoorva Khare
Associated to every complex reflection group, we construct a lattice of quotients of its braid monoid-algebra, which we term nil-Hecke algebras, and which are obtained by killing a…
Matrix compression along isogenic blocks
Alexander Belton, Dominique Guillot, Apoorva Khare +1
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functoria…
Sign non-reversal property for totally non-negative and totally positive matrices, and testing total positivity of their interval hull
Projesh Nath Choudhury, M. Rajesh Kannan, Apoorva Khare
A matrix is totally positive (or non-negative) of order , denoted (or ), if all minors of size are positive (or non-negative). It is well-known that su…
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…
Simultaneous kernels of matrix Hadamard powers
Alexander Belton, Dominique Guillot, Apoorva Khare +1
In previous work [Adv. Math. 298, pp. 325-368, 2016], the structure of the simultaneous kernels of Hadamard powers of any positive semidefinite matrix were described. Key ingredien…
A Carlitz-von Staudt type theorem for finite rings
Apoorva Khare, Akaki Tikaradze
We compute the th power-sums (for all ) over an arbitrary finite unital ring . This unifies and extends the work of Brawley, Carlitz, and Levine for matrix rings [Duke M…