All Questions
11 questions
7
votes
2
answers
3k
views
On the cohomology ring of the Grassmannian
The basis of Schubert classes for the cohomology ring $H^*(\text{Gr}(m,N))$ of the Grassmannian of $m$-dimensional subspaces of $\mathbb{C}^N$ is indexed by $L(m,N-m)$, the poset of all partitions ...
- 1,446
3
votes
0
answers
233
views
A bridge between the algebraic / differential geometry of $\frak{sl}_2(\mathbb{C})$ and the Sheffer-Appell calculus and combinatorics
In "Four examples of Beilinson-Bernstein localization", Anna Romanov introduces the basis
$m_k = \frac{(-1)^k}{k!} \partial^k \delta $
on p. 9, where $\partial$ is a partial derivative and $\...
- 10.5k
8
votes
1
answer
422
views
Conjecture by Ekedahl on Weyl groups and Abelian varieties
A conjecture was made on p.14 in "Cycle Classes of the E-O Stratification on the Moduli of Abelian Varieties" by Torsten Ekedahl (late, excellent contributor to MO) and Gerard Van Der Geer concerning ...
- 10.5k
10
votes
0
answers
436
views
Commuting matrix variety $[A,B]=0$ - can one geometrically explain divisibility of $F_ q$ point count by high powers of $q$?
$\DeclareMathOperator\Comm{Comm}\DeclareMathOperator\Id{Id}$Consider the variety $\Comm$ of commuting matrices $[A,B]=0$ over some field $K$. It is much studied, and interesting for various reasons.
...
- 24.9k
2
votes
1
answer
255
views
Polya-MacMahon-Burnside's generating function at "-1"
$\mathbb{Z}_n$, as a cyclic subgroup of symmetric group $\mathfrak{S}_n$, acts on $[n] :=\{1, 2,\dots,n\}$. Hence $\Bbb{Z}_n$ permutes the elements of the Boolean algebra $2^{[n]}$ of all subsets of $[...
- 43.2k
1
vote
0
answers
96
views
Finding stable ideals of $\mathbb{F}_3[[X,S]]$ by group action
Let $k > 1$ be a positive integer and define the action $\sigma_k$ on $\mathbb{F}_3[[X,S]]$ by:
$\sigma_k: X \mapsto X + S + X^k$
$\sigma_k: S \mapsto S + S^3$.
Conjecture: There exists a ...
- 25.8k
4
votes
1
answer
491
views
What is the permutation group generated by those three given morphisms of the affine space $\mathbb{F}_q^3$?
Let $\mathbb{A}^3 = \mathbb{F}_q^3$. Consider the following three functions $\mathbb{A}^3\to\mathbb{A}^3$:
\begin{eqnarray*}
h: (x, y, z) &\mapsto& (x, y, xy - z) \\
u: (x, y, z) &\mapsto&...
- 22.5k
3
votes
1
answer
607
views
Automorphism groups of indefinite non-unimodular integer lattices
Does anyone know of any papers in which structural aspects of the orthogonal group of some indefinite non-unimodular integral lattice are calculated? The exact lattice isn't so important and they don'...
CommunityBot
- 1
2
votes
2
answers
533
views
elements in the weyl group
Let W be the Weyl a group of a semisimple simply connected group over C.
Let I={1,...,r} the set of simple roots.
For $w\in W$, I denote by supp(w) the subset of I corresponding to the simple ...
- 3,532
5
votes
0
answers
268
views
Unicity of branched covering of sphere, and Hurwitz numbers
Hurwitz's encoding counts the number of branched self-coverings of a sphere, with prescribed ramification degrees at the critical points, as numbers of factorizations of the identity in a symmetric ...
- 2,519
12
votes
0
answers
529
views
A commutative monoid associated with a finite abelian group
Let $M$ be a finite abelian group, and denote by $e_m$, for $m \in M$, the canonical basis of $\mathbb{Z}^M$. For $m, n \in M$ define elements $v_{m,n} \in \mathbb{Z}^M/\langle e_0\rangle$ as
$$
v_{m,...
- 181