Multiplicity-Free Key Polynomials

Coxeter combinatorics and spherical Schubert geometry

“…The proof of this result is found in the companion paper [HY20], where we also derive a multiplicity-free result about the quasi-key polynomials of S. Assaf-D. Searles [AS18].…”

“…The proof is given in the companion paper [HY20]. The following problem asks for a complete generalization of Theorem 4.10:…”

“…The permutations w ∈ S 4 such that wλ = α are 3412, 4312, 3421, 4321, but each of these contains 321 or 3412. In [HY20], we prove Theorem 4.10 using a different, purely combinatorial approach. Third, we examine the following observation that is immediate from Theorem 4.13(II): Corollary 4.17.…”

“…A consequence of (VI) is (VII) Theorem 4.16, which gives sufficient conditions close to those of (V) for a key polynomial to be split multiplicity-free. In comparison to [HY20], the geometric and representation-theoretic input of (VI) allows for a relatively short proof.…”