OS Reelle Geometrie und Algebra: The projective coinvariant algebra

Freitag, 26. April 2024
13:30 bis 15 Uhr

F 426

Veranstaltet von
Mateusz Michalek

Vortragende Person/Vortragende Personen:
Balázs Szendroi

The coinvariant algebra, the quotient of the coordinate ring of (A^1)^n=A^n by the ideal generated by positive degree invariant
polynomials, plays a basic role in algebraic combinatorics and the representation theory of the symmetric group S_n, equipping its regular
representation with a graded algebra structure. Using the coordinate ring of (P^1)^n in its Segre embedding, I will introduce a degeneration
of the coinvariant algebra, the projective coinvariant algebra, which gives a bigraded structure on the regular representation of S_n with
interesting Frobenius character that generalises a classical result of Lusztig and Stanley. I will also show how this algebra contains bigraded
versions of partial coinvariant algebras, coming from coordinate rings of all possible Segre embeddings corresponding to decompositions of n.