Results 41 to 50 of about 27,072 (238)

Cycle Intersection for SOp,q-Flag Domains

International Journal of Mathematics and Mathematical Sciences, 2020
A real form G0 of a complex semisimple Lie group G has only finitely many orbits in any given compact G-homogeneous projective algebraic manifold Z=G/Q.
Faten Abu Shoga
doaj   +1 more source

The degree of a Schubert variety

Advances in Mathematics, 2003
Studying integration along Bott-Samelson cycles the author proves the following beautiful explicit formula for the degree of the Schubert variety \(X_w\) in the flag manifold \(G/T\) associated to an element \(w\) in the Weyl group: Let \(b_w\) be the Kähler sequence and \(A_w\) the Cartan matrix then, \[ \sum \frac{k!b_1^{r_1}\cdots b_k^{r_k}}{r_1 ...
openaire   +2 more sources

On the birational geometry of Schubert varieties [PDF]

Bulletin de la Société mathématique de France, 2015
14 pages, v2: Several small corrections. Accepted for publication in "Bulletin de la SMF"
openaire   +2 more sources

Kazhdan-Lusztig polynomials of boolean elements [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
We give closed combinatorial product formulas for Kazhdan–Lusztig poynomials and their parabolic analogue of type $q$ in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan–Lusztig theory, J.
Pietro Mongelli
doaj   +1 more source

Frobenius splitting and geometry of $G$-Schubert varieties

, 2007
Let $X$ be an equivariant embedding of a connected reductive group $G$ over an algebraically closed field $k$ of positive characteristic. Let $B$ denote a Borel subgroup of $G$. A $G$-Schubert variety in $X$ is a subvariety of the form $\diag(G) \cdot V$,
He, Xuhua, Thomsen, Jesper Funch
core   +4 more sources

Intersections of Schubert Varieties

Journal of Algebra, 1996
The Schubert calculus on a Grassmannian is a very well known topic. In fact, intersection theory on a Grassmannian is done in an algebraic-combinatorial way via Schur polynomials. On a general flag manifold, a canonical cell decomposition and a duality result for the corresponding closures of the cells (i.e. the Schubert varieties) are known.
openaire   +2 more sources

Geometric crystals on Schubert varieties [PDF]

Journal of Geometry and Physics, 2005
25 ...
openaire   +2 more sources

Permutations with Kazhdan-Lusztig polynomial $ P_id,w(q)=1+q^h$ [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
Using resolutions of singularities introduced by Cortez and a method for calculating Kazhdan-Lusztig polynomials due to Polo, we prove the conjecture of Billey and Braden characterizing permutations w with Kazhdan-Lusztig polynomial$ P_id,w(q)=1+q^h$ for
Alexander Woo
doaj   +1 more source

On Tangent Spaces to Schubert Varieties

Journal of Algebra, 2000
Let \(G\) be a semi-simple, simply connected, algebraic group, \(T\) a maximal torus in \(G\), \(W=N_G(T)/T\) the Weyl group and \(B\) a Borel subgroup of \(G\) containing \(T\). For \(w\in W\), let \(e_w\) be the point of \(G/B\) corresponding to the coset \(wB\) and let \(X(w)\) be the associated Schubert variety, i.e., the Zariski closure of \(Be_w\)
openaire   +3 more sources

Deodhar Elements in Kazhdan-Lusztig Theory [PDF]

Discrete Mathematics & Theoretical Computer Science, 2008
The Kazhdan-Lusztig polynomials for finite Weyl groups arise in representation theory as well as the geometry of Schubert varieties. It was proved very soon after their introduction that they have nonnegative integer coefficients, but no simple all ...
Brant Jones
doaj   +1 more source