Generalised Cartan invariants of symmetric groups
نویسندگان
چکیده
منابع مشابه
Cartan Invariants of Symmetric Groups and Iwahori-hecke Algebras
Külshammer, Olsson and Robinson conjectured that a certain set of numbers determined the invariant factors of the `-Cartan matrix for Sn (equivalently, the invariant factors of the Cartan matrix for the Iwahori-Hecke algebra Hn(q), where q is a primitive `th root of unity). We call these invariant factors Cartan invariants. In a previous paper, the second author calculated these Cartan invarian...
متن کاملCartan Invariants
It is safe to say that the theory of modular representations of finite groups is not a part of the average mathematician's toolkit. Matrix representations of finite groups over the complex field, and the resulting characters (traces of matrices), occur rather widely in both pure and applied mathematics. But replacing complex numbers by elements of a finite or other field of prime characteristic...
متن کاملRational Homotopy Groups of Generalised Symmetric Spaces
We obtain explicit formulas for the rational homotopy groups of generalised symmetric spaces, i.e., the homogeneous spaces for which the isotropy subgroup appears as the fixed point group of some finite order automorphism of the group. In particular, this gives explicit formulas for the rational homotopy groups of all classical compact symmetric spaces.
متن کاملThe Vector Invariants of Symmetric Groups
LetR be a commutative ring and let n,m be two positive integers. Let AR(n,m) := R[x11, . . . , x1m, . . . , xn1, . . . , xnm] be the polynomial ring in the commuting independent variables x11, . . . , x1m, . . . , xn1, . . . , xnm with coefficients in R. The symmetric group on n letters Sn acts on AR(n,m) by means of σ(xij) = xσ(i) j for all σ ∈ Sn and i = 1, . . . , n ; j = 1, . . . , m. Let u...
متن کاملA Note on Cartan Matrices for Symmetric Groups
Using generating functions a very simple explicit formula for the determinants of the p-Cartan matrices of symmetric groups is given. Our method works also when p is a composite number.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2014
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-2014-06176-x