# The Grothendieck group of G-equivariant modules over coordinate rings of G-orbits

J. Klimek; W. Kraśkiewicz; J. Weyman

Colloquium Mathematicae (1998)

- Volume: 78, Issue: 1, page 105-118
- ISSN: 0010-1354

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topKlimek, J., Kraśkiewicz, W., and Weyman, J.. "The Grothendieck group of G-equivariant modules over coordinate rings of G-orbits." Colloquium Mathematicae 78.1 (1998): 105-118. <http://eudml.org/doc/210595>.

@article{Klimek1998,

author = {Klimek, J., Kraśkiewicz, W., Weyman, J.},

journal = {Colloquium Mathematicae},

keywords = {categories of graded finitely generated modules; complex connected reductive algebraic groups; coordinate rings; Grothendieck groups; Euler characters of sheaves; global sections of line bundles},

language = {eng},

number = {1},

pages = {105-118},

title = {The Grothendieck group of G-equivariant modules over coordinate rings of G-orbits},

url = {http://eudml.org/doc/210595},

volume = {78},

year = {1998},

}

TY - JOUR

AU - Klimek, J.

AU - Kraśkiewicz, W.

AU - Weyman, J.

TI - The Grothendieck group of G-equivariant modules over coordinate rings of G-orbits

JO - Colloquium Mathematicae

PY - 1998

VL - 78

IS - 1

SP - 105

EP - 118

LA - eng

KW - categories of graded finitely generated modules; complex connected reductive algebraic groups; coordinate rings; Grothendieck groups; Euler characters of sheaves; global sections of line bundles

UR - http://eudml.org/doc/210595

ER -

## References

top- [A] M. Aschbacher, The 27-dimensional module for E_6. I, Invent. Math. 89 (1987), 159-195. Zbl0629.20018
- [D] M. Demazure, A very simple proof of Bott's theorem, ibid. 33 (1976), 271-272. Zbl0383.14017
- [H-U] R. Howe and T. Umeda, The Capelli identity, the double commutant theorem, and multiplicity free actions, Math. Ann. 290 (1991), 565-619. Zbl0733.20019
- [I] J. Igusa, A classification of spinors up to dimension twelve, Amer. J. Math. 92 (1970), 997-1028. Zbl0217.36203
- [K] V. Kac, Some remarks on nilpotent orbits, J. Algebra 64 (1980), 190-213. Zbl0431.17007
- [W] J. Weyman, The Grothendieck group of GL(F)×GL(G)-equivariant modules over the coordinate ring of determinantal varietes, Colloq. Math. 76 (1998), 243-263. Zbl0945.13006

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