5. Macdonald polynomials

Problem 5.1.
What are Schur expansions of projector closures at the category level and what are their connections to Macdonald theory? 
Problem 5.3.
Let $P\in SYT(\lambda)$, $Q\in SYT(\mu)$ relate $Hom(tr(P),tr(Q))$ to the Macdonald inner product. 
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.