Calculus of Finite Differences - eDisk

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– p. 16/?Here are results about the primitive ideals of ourdown-up algebra.Theorem. Suppose p(x) is not the constantpolynomial. Let λ ∈ C. Then the annihilator of V (λ)is a primitive ideal. All other primitive ideals areannihilators of finite-dimensional simple modules. Allfinite-dimensional simple modules are quotients ofVerma modules.So the situation in this case is quite similar to the caseof enveloping algebras of semisimple Lie algebras.
– p. 17/?The special case where p(x) is constant is most easilydescribed by an explicit list.Theorem. Suppose p(x) is the constant polynomial.The primitive ideals in this case are 〈u〉, 〈d〉,〈u,d,h−λ〉, where λ ∈ C, and 〈ud −c〉, where c ≠ 0.
Page 1 and 2: - p. 1/?Calculus of Finite Differen
Page 3: - p. 2/?There are many similarities
Page 6 and 7: - p. 3/?ThenThis should look famili
Page 8 and 9: - p. 4/?The calculus of finite diff
Page 10 and 11: Twenty years later. . .- p. 5/?
Page 12 and 13: - p. 6/?Down-up AlgebrasDown-up alg
Page 18 and 19: - p. 8/?Research aim: determine the
Page 20 and 21: - p. 9/?Side remark: the theory of
Page 22 and 23: - p. 10/?Let’s take the case r =
Page 24 and 25: Annihilators of simple Verma module
Page 26 and 27: - p. 12/?First step: find a central
Page 28 and 29: - p. 13/?Say ud − p(h) commutes w
Page 30 and 31: - p. 15/?The polynomial p is more u

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