Lowest $\mathfrak {sl}(2)$-types in $\mathfrak {sl}(n)$-representations
نویسندگان
چکیده
منابع مشابه
Biological implications of $\mathfrak{so}(2,1)$ symmetry in exact solutions for a self-repressing gene
We chemically characterize the symmetries underlying the exact solutions of a stochastic negatively self-regulating gene. The breaking of symmetry at low molecular number causes three effects. Average protein number differs from the deterministically expected value. Bimodal probability distributions appear as the protein number becomes a readout of the ON/OFF state of the gene. Two branches of ...
متن کاملOn weakly $mathfrak{F}_{s}$-quasinormal subgroups of finite groups
Let $mathfrak{F}$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly $mathfrak{F}_{s}$-quasinormal in $G$ if $G$ has an $S$-quasinormal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $(Hcap T)H_{G}/H_{G}leq Z_{mathfrak{F}}(G/H_{G})$, where $Z_{mathfrak{F}}(G/H_{G})$ denotes the $mathfrak{F}$-hypercenter of $G/H_{G}$. In this paper, we study the structur...
متن کاملOn Minuscule Representations and the Principal Sl2
We study the restriction of minuscule representations to the principal SL2, and use this theory to identify an interesting test case for the Langlands philosophy of liftings. In this paper, we review the theory of minuscule co-weights λ for a simple adjoint group G over C, as presented by Deligne [D]. We then decompose the associated irreducible representation Vλ of the dual group Ĝ, when restr...
متن کاملPlethysm and fast matrix multiplication
Motivated by the symmetric version of matrix multiplication we study the plethysm $S^k(\mathfrak{sl}_n)$ of the adjoint representation $\mathfrak{sl}_n$ of the Lie group $SL_n$. In particular, we describe the decomposition of this representation into irreducible components for $k=3$, and find highest weight vectors for all irreducible components. Relations to fast matrix multiplication, in part...
متن کاملA Howe-type correspondence for the dual pair (sl2, sln) in sl2n
In this article, we study the decomposition of weight–sl2n–modules of degree 1 to a dual pair (sl2, sln). We show that in some generic cases we have an explicit branching rule leading to a Howe–type correspondence between simple highest weight modules. We also give a Howe–type correspondence in the non–generic case. This latter involves some (non simple) Verma modules. Let g denote a reductive ...
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: Representation Theory of the American Mathematical Society
سال: 2017
ISSN: 1088-4165
DOI: 10.1090/ert/492