| Ամփոփում: | <p>This thesis investigates the image of modules of rational Cherednik algebra under the KZ functor and its the compatibility with the unitarity conditions of modules of cyclotomic Hecke algebras. The special case of type A has been well-studied in the literature. Here we aim to generalize the result to rational Cherednik algebras of <em>G</em>(<em>l</em>, 1, <em>n</em>) with generic parameters, and postulate that the KZ functor preserves unitarity. The approach is via the isomorphism between the KZ functor and the direct sum of generalized weight space functors, which leads to the introduction of weighted Khovanov-Lauda-Rouquier (KLR) algebras encoding the action of the intertwining operators. The cyclotomic Hecke algebra whose representations are images under the KZ functor is isormorphic to the cyclotomic KLR algebra as a subalgebra of the weighted KLR algebra. We use this subalgebra as a bridge to discuss how the image of the direct sum of generalized weight space functors becomes a representation of the cyclotomic Hecke algebra, and show that KZ (<em>M<sub>c</sub></em>(λ)) ≅ <em>V<sup>λtr</sup></em> for generic parameters. Then we pass the *-operation on the rational Cherednik algebra to the cyclotomic Hecke algebra. We compare the *-operation with the star-operation that defines unitarity of cyclotomic Hecke algebras. Furthermore, we prove a stronger statement by equating the asymptotic signature of the Hermitian form <em>β<sub>c,λ</sub></em> of rational Cherednik algebras with the signature of Hermitian forms of cyclotomic Hecke algebras.</p>
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