Characters for the Permutation Group of Degree n using Specht Module and Semi Standard Young Tableaux
نویسنده
چکیده
For any partition, the corresponding Specht module is the sub module of permutation module spanned by the poly-tabloids. The Specht modules for a partition of a positive integer n form a complete list of irreducible representations of permutation group of degree n. The Semi-Standard Young Tableau (SSYT), on n -symbols are one type of combinatorial objects occur naturally in many computational problems in Science, Engineering and Technology, which have one-to-one correspondence with Gelfand–Tzetlin bases set of the Unitary group U (n).In this paper, we propose a method to construct character table of permutation group of degree n using Specht module and Semi Standard Young Tableaux. This method is illustrated with an example using a partition of degree 5 in permutation group S5.
منابع مشابه
Construction of Graded Covariant GL(m/n) Modules Using Tableaux
Irreducible covariant tensor modules for the Lie supergroups GL(m/n) and the Lie superalgebras gl(m/n) and sl(m/n) are obtained through the use of Young tableaux techniques. The starting point is the graded permutation action, first introduced by Dondi and Jarvis, on V. The isomorphism between this group of actions and the symmetric group Sl enables the graded generalization of the Young symmet...
متن کاملEnumeration of Semi { Standard Young Tableaux
Standard tableaux. A Young tableau (also known as a standard tableau) is an arrangement of distinct integers in an array of left justiied rows, such that the entries of each row are in increasing order from left to right and the entries of each column are in increasing order from bottom to top 2. For instance, here is an array of size 15: 11 4 8 12 14 3 6 7 13 1 2 5 9 10 15 : In general a table...
متن کاملModular irreducible representations of the symmetric group as linear codes
We describe a particularly easy way of evaluating the modular irreducible matrix representations of the symmetric group. It shows that Specht’s approach to the ordinary irreducible representations, along Specht polynomials, can be unified with Clausen’s approach to the modular irreducible representations using symmetrized standard bideterminants. The unified method, using symmetrized Specht pol...
متن کاملGraphical Approach to Index and Retrieve Standard Young Tableaux
The Standard Young Tableaux are used to label the basis vectors of the standard or Young Yamanouchi basis of the symmetric group. There is a one to one correspondence between the eigen values of the Complete Set of Commuting Operators-I (CSCO-I) of Symmetric group of degree n (Sn) and the Standard Young Tableaux(SYT). In this paper, a new graphical method to index and retrieve the standard Youn...
متن کاملPermutation resolutions for Specht modules
For every composition λ of a positive integer r , we construct a finite chain complex whose terms are direct sums of permutation modules M for the symmetric group Sr with Young subgroup stabilizers Sμ. The construction is combinatorial and can be carried out over every commutative base ring k. We conjecture that for every partition λ the chain complex has homology concentrated in one degree (at...
متن کامل