On Extensions of supersingular representations of ${\rm SL}_2(\mathbb{Q}_p)$

TL;DR

This paper computes the dimensions of extension groups between supersingular representations of SL_2(Q_p) for primes greater than 5, advancing understanding of their structure and relationships.

Contribution

It provides explicit calculations of Ext^1 dimensions between supersingular representations of SL_2(Q_p) for p > 5, a previously uncharted aspect.

Findings

Calculated Ext^1 dimensions for pairs of supersingular representations

Established results for primes p > 5

Enhanced understanding of the representation theory of SL_2(Q_p)

Abstract

In this note for $p>5$ we calculate the dimensions of ${\rm Ext}^1_{{\rm SL}_2(\mathbb{Q}_p)}(\tau, \sigma)$ for any two irreducible supersingular representations $\tau$ and $\sigma$ of ${\rm SL}_2(\mathbb{Q}_p)$.