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## DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3 (WITH AN APPENDIX BY C.M. RINGEL)

#### C. Bowman [1] , S. R. Doty [2] , S. Martin [3]

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We give an algorithm for working out the indecomposable direct summands in a Krull–Schmidt decomposition of a tensor product of two simple modules for G = SL3 in characteristics 2 and 3. It is shown that there is a finite family of modules such that every such indecomposable summand is expressible as a twisted tensor product of members of that family. Along the way we obtain the submodule structure of various Weyl and tilting modules. Some of the tilting modules that turn up in characteristic 3 are not rigid; these seem to provide the first example of non-rigid tilting modules for algebraic groups. These non-rigid tilting modules lead to examples of non-rigid projective indecomposable modules for Schur algebras, as shown in the Appendix. Higher characteristics (for SL3) will be considered in a later paper.
Algebraic groups, tilting modules, Weyl modules, quivers
Other ID JA36VB37HC Articles Author: C. Bowman Author: S. R. Doty Author: S. Martin
 Bibtex @ { ieja266323, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Abdullah HARMANCI}, year = {2011}, volume = {9}, pages = {177 - 219}, doi = {}, title = {DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3 (WITH AN APPENDIX BY C.M. RINGEL)}, key = {cite}, author = {Bowman, C. and Doty, S. R. and Martin, S.} } APA Bowman, C , Doty, S , Martin, S . (2011). DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3 (WITH AN APPENDIX BY C.M. RINGEL). International Electronic Journal of Algebra, 9 (9), 177-219. Retrieved from http://dergipark.org.tr/ieja/issue/25202/266323 MLA Bowman, C , Doty, S , Martin, S . "DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3 (WITH AN APPENDIX BY C.M. RINGEL)". International Electronic Journal of Algebra 9 (2011): 177-219 Chicago Bowman, C , Doty, S , Martin, S . "DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3 (WITH AN APPENDIX BY C.M. RINGEL)". International Electronic Journal of Algebra 9 (2011): 177-219 RIS TY - JOUR T1 - DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3 (WITH AN APPENDIX BY C.M. RINGEL) AU - C. Bowman , S. R. Doty , S. Martin Y1 - 2011 PY - 2011 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 177 EP - 219 VL - 9 IS - 9 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3 (WITH AN APPENDIX BY C.M. RINGEL) %A C. Bowman , S. R. Doty , S. Martin %T DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3 (WITH AN APPENDIX BY C.M. RINGEL) %D 2011 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 9 %N 9 %R %U ISNAD Bowman, C. , Doty, S. R. , Martin, S. . "DECOMPOSITION OF TENSOR PRODUCTS OF MODULAR IRREDUCIBLE REPRESENTATIONS FOR SL3 (WITH AN APPENDIX BY C.M. RINGEL)". International Electronic Journal of Algebra 9 / 9 (June 2011): 177-219.