A. Melnikov

activity

20032018

most citedOn the singularity of the irreducible components of a Springer fiber in sl(n)

33 citations · 52 across the 13 of their papers we have counts for

collaborators

16 papers

math.RT2018

On the existence of smooth orbital varieties in simple Lie algebras

Lucas Fresse, Anna Melnikov

The orbital varieties are the irreducible components of the intersection between a nilpotent orbit and a Borel subalgebra of the Lie algebra of a reductive group. There is a geomet…

math.CO2018

The components of the singular locus of a component of a Springer fiber over x^2 = 0

Ronit Mansour, Anna Melnikov

For $x \in E n d (K^{n})$ satisfying $x^{2} = 0$ let $F_{x}$ be the variety of full flags stable under the action of $x$ (Springer fiber over $x$ ). The full classification of the components…

math.RT2016

B-orbits in abelian nilradicals of types B, C and D: towards a conjecture of Panyushev

Nurit Barnea, Anna Melnikov

Let $B$ be a Borel subgroup of a semisimple algebraic group $G$ and let $m$ be an abelian nilradical in $b = Lie (B)$ . Using subsets of strongly orthogonal…

math.RT2015

B-orbits of square zero in nilradical of the symplectic algebra

Nurit Barnea, Anna Melnikov

Let $S P_{n} (C)$ be the symplectic group and $sp_{n} (C)$ its Lie algebra. Let $B$ be a Borel subgroup of $S P_{n} (C)$ , $b = Lie (B)$ an…

math.AG2009

Some characterizations of singular components of Springer fibers in the two-column case

Lucas Fresse, Anna Melnikov

Let $u$ be a nilpotent endomorphism of a finite dimensional $C$ -vector space. The set $F_{u}$ of $u$ -stable complete flags is a projective algebraic variety calle…

math.AG2009★ 33 cited

On the singularity of the irreducible components of a Springer fiber in sl(n)

Lucas Fresse, Anna Melnikov

Let $B_{u}$ be the Springer fiber over a nilpotent endomorphism $u \in E n d (C^{n})$ . Let $J (u)$ be the Jordan form of $u$ regarded as a partition of $n$ . The irreduci…