scholarly journals Morava K(s)*-rings of the extensions of Cp by the products of good groups under diagonal action

2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Malkhaz Bakuradze
Keyword(s):  
Diagonal Action

AbstractThis note provides a theorem on good groups in the sense of Hopkins–Kuhn–Ravenel [J. Amer. Math. Soc. 13 (2000), no. 3, 553–594] and some relevant examples.

scholarly journals Towards a classification of rigid product quotient varieties of Kodaira dimension 0

2021 ◽  
Author(s):  
Ingrid Bauer ◽  
Christian Gleissner
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Structure Theorem ◽  
Complete Classification ◽  
Kodaira Dimension ◽  
The Other ◽  
Diagonal Action ◽  
Quotient Varieties ◽  
A Finite Group

AbstractIn this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group G. It is shown that only for $$G = {{\,\mathrm{He}\,}}(3), {\mathbb {Z}}_3^2$$ G = He ( 3 ) , Z 3 2 , and only for dimension $$\ge 4$$ ≥ 4 such an action can be free. A complete classification of the singular quotients in dimension 3 and the smooth quotients in dimension 4 is given. For the other finite groups a strong structure theorem for rigid quotients is proven.

INTERSECTION THEORY ON SYMPLECTIC QUOTIENTS OF PRODUCTS OF SPHERES

2001 ◽  
Vol 12 (01) ◽  
pp. 97-111 ◽  
Author(s):  
TATSURU TAKAKURA
Keyword(s):  
Explicit Formula ◽  
Generating Function ◽  
Cohomology Ring ◽  
Geometric Quantization ◽  
Intersection Theory ◽  
Symplectic Reduction ◽  
Poincare Duality ◽  
Diagonal Action ◽  
Symplectic Quotients ◽  
Products Of Spheres

We present an explicit formula for cohomology intersection pairings on an arbitrary smooth symplectic quotient of products of 2-spheres, by the standard diagonal action of SO3, without using known results on relations in the cohomology ring. By the Poincaré duality, it contains all the information enough to recover the structure of the cohomology ring. Our method is based on the commutativity of geometric quantization and symplectic reduction, originating from a conjecture of Guillemin-Sternberg. In fact, it enables us to derive a formula for the generating function of the intersection pairings.

scholarly journals Coding Parking Functions by Pairs of Permutations

10.37236/1716 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Yurii Burman ◽  
Michael Shapiro
Keyword(s):  
Symmetric Group ◽  
Parking Functions ◽  
Diagonal Action ◽  
New Class ◽  
Diagonal Harmonics ◽  
Admissible Pairs

We introduce a new class of admissible pairs of triangular sequences and prove a bijection between the set of admissible pairs of triangular sequences of length $n$ and the set of parking functions of length $n$. For all $u$ and $v=0,1,2,3$ and all $n\le 7$ we describe in terms of admissible pairs the dimensions of the bi-graded components $h_{u,v}$ of diagonal harmonics ${\Bbb{C}}[x_1,\dots,x_n;y_1,\dots,y_n]/S_n$, i.e., polynomials in two groups of $n$ variables modulo the diagonal action of symmetric group $S_n$.

scholarly journals A polynomial expression for the Hilbert series of the quotient ring of diagonal coinvariants (condensed version)

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
J. Haglund
Keyword(s):  
Hilbert Series ◽  
Quotient Ring ◽  
Rational Functions ◽  
Constant Term ◽  
Diagonal Action ◽  
Integer Coefficients ◽  
Polynomial Expression ◽  
International Audience ◽  
Special Case ◽  
Invent Math

International audience A special case of Haiman's identity [Invent. Math. 149 (2002), pp. 371–407] for the character of the quotient ring of diagonal coinvariants under the diagonal action of the symmetric group yields a formula for the bigraded Hilbert series as a sum of rational functions in $q,t$. In this paper we show how a summation identity of Garsia and Zabrocki for Macdonald polynomial Pieri coefficients can be used to transform Haiman's formula for the Hilbert series into an explicit polynomial in $q,t$ with integer coefficients. We also provide an equivalent formula for the Hilbert series as the constant term in a multivariate Laurent series. Un cas spécial de l'identité de Haiman [Invent. Math. \textbf149 (2002), pp. 371–407] pour le caractère de l'anneau quotient des coinvariants diagonaux sous l'action du groupe symétrique fournit une formule pour la série de Hilbert bigraduée comme somme de fonctions rationnelles en q,t. Dans cet article nous montrons comment une identité de sommation de Garsia et Zabrocki pour les coefficients de Pieri des polynômes de Macdonald peut être utilisée pour transformer la formule de Haiman pour la série de Hilbert en un polynôme explicite en q,t à coefficients entiers. Nous présentons également une formule équivalente pour la série de Hilbert comme terme constant d'une série de Laurent multivariée.

Sign in / Sign up

Export Citation Format

Share Document