Álvaro L. Martínez

activity

20182026

most citedLow-dimensional irreducible rational representations of classical algebraic groups

3 citations · 3 across the 4 of their papers we have counts for

collaborators

4 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 $q$ -Pfaff--Saalschütz identity with applications to quantum groups

Álvaro Gutiérrez, Álvaro L. Martínez, Michał Szwej +1

We present a combinatorial proof of the $q$ -Pfaff--Saalschütz identity by a composition of explicit bijections, in which $q$ -binomial coefficients are interpreted as counting subsp…

math.RT2024

A new modular plethystic $SL_{2} (F)$ -isomorphism $Sym^{N - 1} E \otimes ⋀^{N + 1} Sym^{d + 1} E ≅ Δ^{(2, 1^{N - 1})} Sym^{d} E$

Alvaro L. Martinez, Mark Wildon

Let $F$ be a field and let $E$ be the natural representation of $SL_{2} (F)$ . Given a vector space $V$ , let $Δ^{(2, 1^{N - 1})} V$ be the kernel of the multipli…

math.RT2018★ 3 cited

Low-dimensional irreducible rational representations of classical algebraic groups

Álvaro L. Martínez

Let $G$ be an algebraic group of classical type of rank $l$ over an algebraically closed field $K$ of characteristic $p$ . We list and determine the dimensions of all irreducible $K…

Even and odd minimal categorifications of the nilpotent part of classical and quantum sl(2)

A new bijective proof of the q-Pfaff--Saalschütz identity with applications to quantum groups

A new modular plethystic SL2​(F)-isomorphism SymN−1E⊗⋀N+1Symd+1E≅Δ(2,1N−1)SymdE

Low-dimensional irreducible rational representations of classical algebraic groups

A new bijective proof of the $q$ -Pfaff--Saalschütz identity with applications to quantum groups

A new modular plethystic $SL_{2} (F)$ -isomorphism $Sym^{N - 1} E \otimes ⋀^{N + 1} Sym^{d + 1} E ≅ Δ^{(2, 1^{N - 1})} Sym^{d} E$