Codimensions of T-ideals and Hilbert series of relatively free algebras

Asymptotic behaviour of codimensions of p. i. algebras satisfying Capelli identities

“…Drensky showed in [8] that the cocharacter sequence of A is Young derived, whenever A has a unit. We record that theorem by way of reminding the reader of the definition of Young derived sequences.…”

Multiplicities in the Mixed Trace Cocharacter Sequence of Two 3 × 3 Matrices

“…The multiplicities of the cocharacters of M n (F ), C, T are explicitly found for n = 2 only, by Formanek [9] for M 2 (F ), C, T , and, with different methods, by Drensky [4] for M 2 (F ), see also Procesi [14]. In particular,…”

Asymptotics for the multiplicities in the cocharacters of some PI-algebras

“…Then one considers in a natural way the S n -character of P n (A), denoted ψ n (A), which is called the n-th proper cocharacter of A. A result of Drensky [6,Theorem 2.6] gives the precise relation between the ordinary cocharacters and the proper cocharacters of any PI-algebra A: if ψ p (A) = λ p m λ χ λ , where χ λ is the irreducible S n -character associated to the partition λ n, then…”

“…The multiplicities in the cocharacter sequence of M 2 (F ) were computed in [6], [9], [23]. An inspection of these multiplicities shows that for all n, max µ n m µ = m λ for some λ = (λ 1 , .…”

“…The sequence c n (A) or even its asymptotic behaviour has only been computed for some special algebras [6], [9], [18], [19], [23], [25]; it turns out that it is in general a very hard problem to determine the precise asymptotic behaviour of such a sequence.…”