2,336 reputation
11127
bio website ime.usp.br/~gorodski
location Sao Paulo, Brazil
age 49
visits member for 4 years, 1 month
seen yesterday
I am a Professor at the University of São Paulo. I have mostly worked on the interaction between Lie groups and geometry, more specifically, Lie transformation groups and submanifold geometry, but I am generally interested in different kinds of problems that can be considered from a geometrical viewpoint.

Jun
9
awarded  Nice Answer
May
16
awarded  Yearling
Feb
22
awarded  Nice Answer
Feb
21
comment Image of skew-symmetric bilinear map which is never zero on linearly independent vectors
$b:\Lambda^2\mathbb R^4\to W^3$ whose kernel is $a_{12}=a_{34}$, $a_{14}=a_{23}$, $a_{13}=-a_{24}$, and consider its projectivization $U^2 \subset \mathbb P (\Lambda^2\mathbb R^4)$. Then $U^2$ does not meet $\mathbb G(2,\mathbb R^4)$. On the other hand, $2\dim V - 3 = 5 > 3 = \dim W$.
Feb
21
comment Image of skew-symmetric bilinear map which is never zero on linearly independent vectors
the equation $a_{12}a_{34}-a_{13}a_{24}+a_{14}a_{23}=0$. Construct a linear map
Feb
21
comment Image of skew-symmetric bilinear map which is never zero on linearly independent vectors
I think this is a counter-example: $\mathbb G(2,\mathbb R^4)$ has dim $4$ and embedds in $\mathbb P(\Lambda^2\mathbb R^4)$ which has dim $5$, defined
Feb
21
comment Image of skew-symmetric bilinear map which is never zero on linearly independent vectors
This is way late, but I think the argument works over $\mathbb C$ but not over $\mathbb R$, which is what I wanted. The obvious idea of complexifying $B$ does not seem to preserve the assumption on $B$.
Jan
9
comment Image of skew-symmetric bilinear map which is never zero on linearly independent vectors
Simple and smart, thanks! In fact, the better bound suffices for what I need.
Jan
9
accepted Image of skew-symmetric bilinear map which is never zero on linearly independent vectors
Jan
9
asked Image of skew-symmetric bilinear map which is never zero on linearly independent vectors
Jan
3
awarded  Nice Answer
Oct
23
awarded  Necromancer
Jul
20
comment Calculation with weights of $E_6$
@Jim: Thanks for your comment. I was sloppy: it was to mean $\Gamma$ is a subquotient of $W$. Anyway, I was wrong about the given motivation. Howe and Umeda's paper "The Capelli identity, the double commutant theorem, and multiplicity-free actions" discusses this representation.
Jul
20
revised Calculation with weights of $E_6$
Updated information.
Jul
17
comment Is the Duflo polynomial conjecture open?
I guess the main reference is: Journal of Functional Analysis, Volume 117, Issue 1, October 1993, Pages 174–214, Invariant Differential Operators in Symmetrical Spaces. II. Generalized Harish-Chandra Homomorphism, by C. Torossian.
Jul
12
revised Calculation with weights of $E_6$
Added possible answer.
Jul
11
revised Calculation with weights of $E_6$
Clarified notation.
Jul
11
comment Calculation with weights of $E_6$
@Jim: I meant the Coxeter group of type $A_2$.
Jul
11
comment Calculation with weights of $E_6$
@Vit: No, it is not.
Jul
11
asked Calculation with weights of $E_6$