scholarly journals Highest weight generating functions for Hilbert series

2014 ◽  
Vol 2014 (10) ◽  
Author(s):  
Amihay Hanany ◽  
Rudolph Kalveks
Keyword(s):  
Generating Functions ◽  
Hilbert Series ◽  
Highest Weight

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

scholarly journals Enumerating projective reflection groups

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Riccardo Biagioli ◽  
Fabrizio Caselli
Keyword(s):  
Representation Theory ◽  
Generating Functions ◽  
Special Class ◽  
Hilbert Series ◽  
Weyl Groups ◽  
Reflection Groups ◽  
One Dimensional ◽  
Complex Reflection Groups ◽  
Major Index ◽  
International Audience

International audience Projective reflection groups have been recently defined by the second author. They include a special class of groups denoted G(r,p,s,n) which contains all classical Weyl groups and more generally all the complex reflection groups of type G(r,p,n). In this paper we define some statistics analogous to descent number and major index over the projective reflection groups G(r,p,s,n), and we compute several generating functions concerning these parameters. Some aspects of the representation theory of G(r,p,s,n), as distribution of one-dimensional characters and computation of Hilbert series of some invariant algebras, are also treated. Les groupes de réflexions projectifs ont été récemment définis par le deuxième auteur. Ils comprennent une classe spéciale de groupes notée G(r,p,s,n), qui contient tous les groupes de Weyl classiques et plus généralement tous les groupes de réflexions complexes du type G(r,p,n). Dans ce papier on définit des statistiques analogues au nombre de descentes et à l'indice majeur pour les groupes G(r,p,s,n), et on calcule plusieurs fonctions génératrices. Certains aspects de la théorie des représentations de G(r,p,s,n), comme la distribution des caractères linéaires et le calcul de la série de Hilbert de quelques algèbres d'invariants, sont aussi abordés.

scholarly journals Highest weight generating functions for hyperKähler T ⋆(G/H) spaces

2016 ◽  
Vol 2016 (10) ◽  
Author(s):  
Amihay Hanany ◽  
Sanjaye Ramgoolam ◽  
Diego Rodriguez-Gomez
Keyword(s):  
Generating Functions ◽  
Highest Weight

scholarly journals Factorised 3d $$ \mathcal{N} $$ = 4 orthosymplectic quivers

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Mohammad Akhond ◽  
Federico Carta ◽  
Siddharth Dwivedi ◽  
Hirotaka Hayashi ◽  
Sung-Soo Kim ◽  
...  
Keyword(s):  
Moduli Space ◽  
Gauge Theories ◽  
Hilbert Series ◽  
Point Of View ◽  
Coulomb Branch ◽  
Dual Pairs ◽  
Superconformal Field Theories ◽  
Quiver Gauge Theory ◽  
Highest Weight ◽  
Exceptional Sequences

Abstract We study the moduli space of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d $$ \mathcal{N} $$ N = 1 superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expansion.

POTENSI PENGEMBANGAN SADE SEBAGAI DESA WISATA LOMBOK

2016 ◽  
Vol 20 (2) ◽  
pp. 69-82
Author(s):  
W. Suprihatin ◽  
H. Hailuddin
Keyword(s):  
Analytical Hierarchy Process ◽  
Environmental Aspect ◽  
Priority Level ◽  
Highest Weight ◽  
Local Tradition ◽  
Tourist Village ◽  
Hierarchy Process ◽  
Initial Pattern

The background of the problems in this study is the decreasing quality of Sade hamlet amid rising tourist arrivals. From the environmental aspect, the conditions of the hamlet began to decline, in which the initial pattern of Sade has started a lot of changes towards the deficient and began to leave the local tradition. One effort to improve the condition of Sade hamlet in social, cultural and the environmental aspect is through the formulation of a sustainable structuring, the presence and identity maintaining and making a sustainable Tourism Village. Through analysis of AHP (Analytical Hierarchy Process) by collecting the perceptions of some experts through interviews and questionnaires, obtained by weighting the priority of the experts, namely the preservation of culture as an element of priority-level goals to be achieved in the development of Sade Hamlet as a tourist village at 0,476. While the determination of the level of the main criteria in the achievement of these objectives is the highest weight while maintaining a typical village environment at 0.319. Priority strategies that get the highest weight of the experts is that Sade Hamlet Revitalization with a priority weighting of 0.583. The second priority is the relocation of Hamlet at 0.235. Lowest weighting or last priority is Replication Sade Hamlet at 0.182.

RESPON PERTUMBUHAN DAN PRODUKSI TANAMAN UBI KAYU VARIETAS ADIRA 1 DAN ADIRA 4 TERHADAP PUPUK ORGANIK HAYATI VAM MIKORHYZA

2019 ◽  
Vol 1 (2) ◽  
pp. 41-47
Author(s):  
Ferdinandus Ronsumbre ◽  
Yosefina Mangera ◽  
Ni luh Sri Suryaningsih
Keyword(s):  
Analysis Of Variance ◽  
Good Growth ◽  
Random Design ◽  
Highest Weight

The research of response of growth and production of cassava plants of variety Adira 1 and Adira 4 towards Vam Mikorhyza fertilizer is conducted to figure out the response of plants towards fertilizer given so that the plants can reach good growth and production. This research used the random design of the factorial group, which consists of 2 factors. The first factor was the variety, consists of 2 variety they were variety Adira 1 (V1) and variety Adira 4 (V2) and the second factor was fertilizer, consists of 2 fertilizer they were Vam Mikorhyza (P1) and compost (P2). Each factor was combined into four treatment combinations which consist of treatment V1P1, V1P2, V2P1, and V2P2. The four treatment combinations were repeated 3 times so it was obtained 12 partition units of the experiment, which was analyzed by analysis of variance. The highest weight of tubers production obtain from Adira 4 variety (V2) was the production reach 28,833 ton ha-1, while the lowest one obtain from Adira 1 variety (V1) with average produced of tubers only 24,683 ton ha-1.

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