3 papers
math.QA2026
Even and odd minimal categorifications of the nilpotent part of classical and quantum sl(2)
Mikhail Khovanov, Alvaro L. Martinez, Fan Zhou
We write down generators and relations for a minimalist version of the nilHecke category which allows us to categorify the divided powers of a generating functor. We then classify…
math.CO2025
A new bijective proof of the -Pfaff--Saalschütz identity with applications to quantum groups
Álvaro Gutiérrez, Álvaro L. Martínez, Michał Szwej +1
We present a combinatorial proof of the -Pfaff--Saalschütz identity by a composition of explicit bijections, in which -binomial coefficients are interpreted as counting subsp…
math.RT2018
Low-dimensional irreducible rational representations of classical algebraic groups
Álvaro L. Martínez
Let be an algebraic group of classical type of rank over an algebraically closed field of characteristic . We list and determine the dimensions of all irreducible $K…