Geodesic
On Multiplicities of Points on Schubert Varieties in Grassmannians
Séminaire lotharingien de combinatoire, Tome 45 (2000-2001)

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We answer some questions related to multiplicity formulas by Rosenthal and Zelevinsky and by Lakshmibai and Weyman for points on Schubert varieties in Grassmannians. In particular, we give combinatorial interpretations in terms of nonintersecting lattice paths of these formulas, which makes the equality of the two formulas immediately obvious. Furthermore we provide an alternative determinantal formula for these multiplicities, and we show that they count semistandard tableaux of unusual shapes. 

@article{SLC_2000-2001_45_a2,
     author = {Christian Krattenthaler},
     title = {On {Multiplicities} of {Points} on {Schubert} {Varieties} in {Grassmannians}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {45},
     year = {2000-2001},
     url = {http://geodesic.mathdoc.fr/item/SLC_2000-2001_45_a2/}
}
TY  - JOUR
AU  - Christian Krattenthaler
TI  - On Multiplicities of Points on Schubert Varieties in Grassmannians
JO  - Séminaire lotharingien de combinatoire
PY  - 2000-2001
VL  - 45
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2000-2001_45_a2/
ID  - SLC_2000-2001_45_a2
ER  - 
%0 Journal Article
%A Christian Krattenthaler
%T On Multiplicities of Points on Schubert Varieties in Grassmannians
%J Séminaire lotharingien de combinatoire
%D 2000-2001
%V 45
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2000-2001_45_a2/
%F SLC_2000-2001_45_a2
Christian Krattenthaler. On Multiplicities of Points on Schubert Varieties in Grassmannians. Séminaire lotharingien de combinatoire, Tome 45 (2000-2001). http://geodesic.mathdoc.fr/item/SLC_2000-2001_45_a2/