Hall-Littlewood Polynomials, Affine Schubert Series, and Lattice Enumeration

Explore Hall-Littlewood-Schubert series, a new class of multivariate generating functions that combine semistandard Young tableaux with polynomials resembling classical Hall-Littlewood polynomials. Discover their applications to counting problems in algebra, geometry, and number theory, with particular focus on affine Schubert series as integral analogues of Poincaré polynomials. Learn how these series enumerate rational points over finite fields of classical Schubert varieties, which parametrize subspaces of vector spaces through intersection dimensions with fixed reference flags. Gain understanding of this advanced mathematical framework through accessible explanations that require no prior familiarity with the technical vocabulary, making complex concepts in algebraic combinatorics and geometric enumeration approachable for a broader mathematical audience.