A Note on Parabolic Subgroups and the Steenrod Algebra Action

2008 ◽  
Vol 15 (04) ◽  
pp. 689-698
Author(s):  
Nondas E. Kechagias
Keyword(s):  
Steenrod Algebra ◽  
Parabolic Subgroups ◽  
Generating Set ◽  
Modular Invariants ◽  
Dickson Algebra

The ring of modular invariants of parabolic subgroups has been described by Kuhn and Mitchell using Dickson algebra generators. We provide a new generating set which is closed under the Steenrod algebra action along with the relations between these elements.

Flag modules and the hit problem for the Steenrod algebra

2009 ◽  
Vol 147 (1) ◽  
pp. 143-171 ◽  
Author(s):  
G. WALKER ◽  
R. M. W. WOOD
Keyword(s):  
Algebraic Topology ◽  
Polynomial Algebra ◽  
Cell Decomposition ◽  
Steenrod Algebra ◽  
Divided Power ◽  
Equivalent Problem ◽  
Generating Set ◽  
Dual Hopf Algebra ◽  
Hit Problem ◽  
Minimal Generating Set

AbstractThe ‘hit problem’ of F. P. Peterson in algebraic topology asks for a minimal generating set for the polynomial algebraP(n) =2[x1,. . .,xn] as a module over the Steenrod algebra2. An equivalent problem is to find an2-basis for the subringK(n) of elementsfin the dual Hopf algebraD(n), a divided power algebra, such thatSqk(f)=0 for allk> 0. The Steenrod kernelK(n) is a2GL(n,2)-module dual to the quotientQ(n) ofP(n) by the hit elements+2P(n). A submoduleS(n) ofK(n) is obtained as the image of a family of maps from the permutation moduleFl(n) ofGL(n,2) on complete flags in ann-dimensional vector spaceVover2. We use the Schubert cell decomposition of the flags to calculateS(n) in degrees$d =\sum_{i=1}^n (2^{\lambda_i}-1)$, where λ1> λ2> ⋅⋅⋅ > λn≥ 0. When λn= 0, we define a2GL(n,2)-module map δ:Qd(n) →Q2d+n−1(n) analogous to the well-known isomorphismQd(n) →Q2d+n(n) of M. Kameko. When λn−1≥ 2, we show that δ is surjective and δ*:S2d+n−1(n)→Sd(n) is an isomorphism.

Polynomials and the mod 2 Steenrod Algebra

2017 ◽  
Author(s):  
Grant Walker ◽  
Reginald M. W. Wood
Keyword(s):  
Steenrod Algebra

Polynomials and the mod 2 Steenrod Algebra

2017 ◽  
Author(s):  
Grant Walker ◽  
Reginald M. W. Wood
Keyword(s):  
Steenrod Algebra

ARITHMETIC TRACES OF NON-HOLOMORPHIC MODULAR INVARIANTS

2010 ◽  
Vol 06 (01) ◽  
pp. 69-87 ◽  
Author(s):  
ALISON MILLER ◽  
AARON PIXTON
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Fourier Coefficients ◽  
Algebraic Numbers ◽  
Heegner Points ◽  
Positive Weight ◽  
Poincare Series ◽  
Half Integral Weight ◽  
Integral Weight ◽  
Modular Invariants

We extend results of Bringmann and Ono that relate certain generalized traces of Maass–Poincaré series to Fourier coefficients of modular forms of half-integral weight. By specializing to cases in which these traces are usual traces of algebraic numbers, we generalize results of Zagier describing arithmetic traces associated to modular forms. We define correspondences [Formula: see text] and [Formula: see text]. We show that if f is a modular form of non-positive weight 2 - 2 λ and odd level N, holomorphic away from the cusp at infinity, then the traces of values at Heegner points of a certain iterated non-holomorphic derivative of f are equal to Fourier coefficients of the half-integral weight modular forms [Formula: see text].

scholarly journals A generating set for the canonical ideal of HKG-curves

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Aristides Kontogeorgis ◽  
Ioannis Tsouknidas
Keyword(s):  
Generating Set ◽  
Canonical Ideal
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