3 research outputs found
Secants of minuscule and cominuscule minimal orbits
We study the geometry of the secant and tangential variety of a cominuscule
and minuscule variety, e.g. a Grassmannian or a spinor variety. Using methods
inspired by statistics we provide an explicit local isomorphism with a product
of an affine space with a variety which is the Zariski closure of the image of
a map defined by generalized determinants. In particular, equations of the
secant or tangential variety correspond to relations among generalized
determinants. We also provide a representation theoretic decomposition of
cubics in the ideal of the secant variety of any Grassmannian
Plethysm and lattice point counting
We apply lattice point counting methods to compute the multiplicities in the
plethysm of . Our approach gives insight into the asymptotic growth of
the plethysm and makes the problem amenable to computer algebra. We prove an
old conjecture of Howe on the leading term of plethysm. For any partition
of 3,4, or 5 we obtain an explicit formula in and for the
multiplicity of in .Comment: 25 pages including appendix, 1 figure, computational results and code
available at http://thomas-kahle.de/plethysm.html, v2: various improvements,
v3: final version appeared in JFoC
Hyperon signatures in the PANDA experiment at FAIR
We present a detailed simulation study of the signatures from the sequential decays of the triple-strange pbar p -> Ω+Ω- -> K+ΛbarK- Λ -> K+pbarπ+K-pπ- process in the PANDA central tracking system with focus on hit patterns and precise time measurement. We present a systematic approach for studying physics channels at the detector level and develop input criteria for tracking algorithms and trigger lines. Finally, we study the beam momentum dependence on the reconstruction efficiency for the PANDA detector