Abstract
We will study the Hall algebra ℋ(Δ) of hereditary orders. We will give an ideal I of such that is isomorphic to the universal enveloping algebra U(𝔤𝔩 n ) (Sec. 1.3). Then we will construct an ℋ(Δ)-module (m ∈ ℕ) by a Hall algebra approach, which restricts to the irreducible U(𝔰𝔩 n )-module with the highest weight mω1 (Sec. 1.4).
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