𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Multiplicities of Schur functions in invariants of two 3×3 matrices

✍ Scribed by Vesselin Drensky; Georgi K. Genov

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
192 KB
Volume
264
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

We relate with any symmetric function f (x, y) ∈ C❏x, y❑ presented as an infinite linear combination of Schur functions

We study the behavior of M(f ) under natural combinatorial and algebraic constructions. In particular, we calculate the multiplicity series for the symmetric algebra of the irreducible GL 2 (C)-module corresponding to the complete symmetric function of degree 3. Our main result is that we have found the explicit form of the multiplicity series for the Hilbert (or Poincaré) series of the algebra of invariants of two 3 × 3 matrices. As a consequence, we have precised the result of Berele on the asymptotics of the multiplicities in the trace cocharacter sequence of two 3 × 3 matrices.

📜 SIMILAR VOLUMES

The structure of the invariant ring of t
The structure of the invariant ring of two matrices of degree 3
✍ Kazunori Nakamoto 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 190 KB

We determine the structure of the invariant ring of two matrices of degree 3. The spectrum of Z[M3 × M3] PGL 3 is isomorphic to a hypersurface of A 11 Z .