On The Ext Groups Between Modules For General Linear Lie Algebra

This paper studies extension groups between certain modules of the general linear algebra gl_n over the integers using the properties of the Weyl modules for the algebraic group GL_n over the integers. Main result is: for any two gl₂(Z) modules K_λand K_μ, Extⁱ(K_λ,K_μ) = 0 for i > d, whereλ= (λ₁,λ₂),μ= (λ₁+d,λ₂-d) . It has very important significance in modular representation theory of gl₂. By the Universal Coefficient Theorem, one can get the information about the Extⁱ(K_λ,K_μ) over an algebraically closed field of characteristic p>0.