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5. Macdonald polynomials


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      Problem 5.1.

      What are Schur expansions of projector closures at the category level and what are their connections to Macdonald theory?


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          Problem 5.2.

          Categorify the modified Macdonald polynomials $\tilde{H_\mu}$.


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              Problem 5.3.

              Let $P\in SYT(\lambda)$, $Q\in SYT(\mu)$ relate $Hom(tr(P),tr(Q))$ to the Macdonald inner product.


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                  Problem 5.4.

                  Find the Macdonald/Schur expansion of the $a$-graded Frobenius character of the parking function space. How does the $tr(T(m,n)$ relate to the parking function module?

                      Cite this as: AimPL: Algebra, geometry, and combinatorics of link homology, available at http://aimpl.org/agclinkhom.