3. Using the commutation relation [7(X), A(Y)] a(H) and induction on k, verify the relation (4.15). 4. Define a vector s

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3 Using The Commutation Relation 7 X A Y A H And Induction On K Verify The Relation 4 15 4 Define A Vector S 1 (34.49 KiB) Viewed 33 times

3. Using the commutation relation [7(X), A(Y)] a(H) and induction on k, verify the relation (4.15). 4. Define a vector space with basis uo, u1.... . Um. Now, define operators (H), (X), and 7(Y) by formula (4.16). Verify by direct computation that the oper- ators defined by (4.16) satisfy the commutation relations (4.11) for sl(2:0). Hint: When dealing with 7 (Y), treat the case of uk, k < m, separately from the case of um, and similarly for (X).