On integral $\mathrm{Ext^2}$ between certain Weyl modules of $\mathrm{GLn}$

Abstract

Consider partitions of the form $λ=(a,1^b)$ and $μ=(a+1,b-1)$,\\ where $a+1>b-1$. In this paper, we determine the extension groups $\mathrm{Ext}_A^2(K_λF,K_μF)$, where $F$ is a free $\mathbb{Z}-$module of finite rank $n$, $K_λF$ and $K_μF$ are the Weyl modules of the general linear group $GL_n(\mathbb{Z})$ corresponding to $λ$ and $μ$, respectively, $A=S_\mathbb{Z}(n,r)$ is the integral Schur algebra and $r=a+b$.

Theorems & Definitions (72)

• Theorem 2.1
• Proposition 2.2
• Theorem 2.3
• Proposition 3.1
• proof
• Proposition 3.2
• Theorem 3.3
• Definition 3.4
• Definition 3.5
• Definition 3.6