\titleofpresentation{One particle $N$-representability}

\presenter{Murat Altunbulak}  %  Name just one speaker, please; collaborators
            %  can be credited in the body of the abstract.

The talk will be a presentation of the joint-paper with
Prof.\ Alexander Klyachko.  The problem in question is about relation
between spectra of a mixed state $\rho$ of $N$ fermion system and
its one point reduced matrix $\rho^{(1)}$. We briefly review the
history of the problem and give two different solutions, one in
terms of linear inequalities on spectra of $\rho$ and $\rho^{(1)}$
and another in terms of irreducible components of certain
plethysms of the unitary group. We combine these solutions to
produce all constraints  on one point reduced matrix of a pure
state for fermion systems up to rank  8. Some of them were
conjectured by Borland and Dennis \cite{altunbulakaBorlandDennis} more than
30 years ago.


\begin{ourbiblio}{99}  %  Delete this environment if you
               %  aren't giving a bibliography.

\bibitem{altunbulakaBorlandDennis} Borland,~R.~E. and Dennis,~K.:
{The conditions on the one-matrix for three-body fermion
wavefunctions with one-rank equal to six}. {J. Phys. B: Atom
Molec. Phys.} \textbf{5},  7--15 (1972)

\end{ourbiblio}

\presenteraddress{Bilkent University }  % The name of a university is fine.

\email{murata@fen.bilkent.edu.tr}

% Delete the next line when you are done.


