scholarly journals A compact presentation for the alternating central extension of the positive part of U_q(sl_2)

2021 ◽  
Author(s):  
Paul M. Terwilliger
Keyword(s):  
Central Extension ◽  
Positive Part

scholarly journals A note on central group extensions

1973 ◽  
Vol 15 (4) ◽  
pp. 428-429 ◽  
Author(s):  
G. J. Hauptfleisch
Keyword(s):  
Abelian Group ◽  
Homomorphic Image ◽  
Free Group ◽  
Central Extension ◽  
Dihedral Group ◽  
Group Extension ◽  
Central Group ◽  
Group Extensions

If A, B, H, K are abelian group and φ: A → H and ψ: B → K are epimorphisms, then a given central group extension G of H by K is not necessarily a homomorphic image of a group extension of A by B. Take for instance A = Z(2), B = Z ⊕ Z, H = Z(2), K = V4 (Klein's fourgroup). Then the dihedral group D8 is a central extension of H by K but it is not a homomorphic image of Z ⊕ Z ⊕ Z(2), the only group extension of A by the free group B.

The positive-part Stein-rule estimator and tests of linear hypotheses

1988 ◽  
Vol 26 (1) ◽  
pp. 49-51 ◽  
Author(s):  
Aman Ullah ◽  
David E.A. Giles
Keyword(s):  
Positive Part ◽  
Tests Of Linear Hypotheses

scholarly journals Facets of the Generalized Cluster Complex and Regions in the Extended Catalan Arrangement of Type $A$

10.37236/3169 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Susanna Fishel ◽  
Myrto Kallipoliti ◽  
Eleni Tzanaki
Keyword(s):  
Simple Root ◽  
Type A ◽  
Cluster Complex ◽  
Integer Partitions ◽  
Positive Part

In this paper we present a bijection between two well known families of Catalan objects: the set of facets of the $m$-generalized cluster complex $\Delta^m(A_n)$ and that of dominant regions in the $m$-Catalan arrangement ${\rm Cat}^m(A_n)$, where $m\in\mathbb{N}_{>0}$. In particular, the map which we define bijects facets containing the negative simple root $-\alpha$ to dominant regions having the hyperplane $\{v\in V\mid\left\langle v,\alpha \right\rangle=m\}$ as separating wall. As a result, it restricts to a bijection between the set of facets of the positive part of $\Delta^m(A_n)$ and the set of bounded dominant regions in ${\rm Cat}^m(A_n)$. Our map is a composition of two bijections in which integer partitions in an $m$-dilated $n$-staircase shape come into play.

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