The canonical basis and the quantum Frobenius morphism
6 pages
English

The canonical basis and the quantum Frobenius morphism

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6 pages
English
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Tout savoir sur nos offres

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  • mémoire - matière potentielle : olivia rossi - doria
The canonical basis and the quantum Frobenius morphism Pierre Baumann Abstract The first goal of this paper is to study the amount of compatibility between two important constructions in the theory of quantized enveloping algebras, namely the canonical basis and the quantum Frobenius morphism. The second goal is to study orders with which the Kashiwara crystal B(∞) of a symmetrizable Kac-Moody algebra can be endowed; these orders are defined so that the transition matrices between bases naturally indexed by B(∞) are lower triangular.
  • convex polytope
  • algebra uq
  • φi
  • b′
  • highest weight vector
  • algebra
  • elements
  • basis
  • weight
  • sequence

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Nombre de lectures 32
Langue English

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Lesson Plan Teachers Name......................................................................................Date.......................................................................... Grade..................................Class(es)....................................................Date(s)...............................................M Tu W Th F Lesson 12.1tivesSE/TWE pp. 45145 Adjec FOCUS Objectives:To identify predicate adjectives and a correctly to describe nouns and pronouns
Bellringer and Motivating Activity, TWE p.
TEACH Teaching Tip, TWE p. 451 Crossreference: Grammar, TWE p. 451 Exploring Language, TWE p. 452
PRACTICE AND ASSESS Answers: Exercises 1 and 2, TWE p. 452
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Bellringer and Motivating Activity, TWE p.
TEACH Grammar Tip, TWE p. 453 Crossreference: Mechanics, TWE p. 453 Critical Thinking, TWE p. 454
PRACTICE AND ASSESS Answers: Exercises 3, 4, 5, TWE p. 454
Additional Resources Bellringer Activities Transparencies Daily Language Practice Transparencies Grammar Practice,p. 20
CLOSE Close activity, TWE p. 454
96Writers Choice:Lesson Plans,Grade
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Assessment Options Tests with Answer Key & Rubrics Unit 12 Pretest, pp. 4546 Testmaker Unit 12 Pretest
Lesson Plan Teachers Name......................................................................................Date.......................................................................... Grade..................................Class(es).....................................................Date(s)...............................................M Tu W Th F Lesson 12.3Comparative and Superlative Ad FOCUS Objectives:To recognize and use comparative and superlativ purpose; to use comparative and superlative adjectives correc
Bellringer and Motivating Activity, TWE p. 455 TEACH Grammar Tip, TWE p. 455 TwoMinute Skill Drill, TWE p. 456 English Language Learners, TWE p. 456 PRACTICE AND ASSESSAdditional Resources Bellringer Activities Transparencies Answers: Exercise 6, TWE p. 456 Daily Language Practice Transparencies TwoMinute Skill Drill Transparencies CLOSE Grammar Practice,p. 21 Close activity, TWE p. 456 Grammar Reteaching,p. 24 Grammar Enrichment,p. 21 Grammar Workbook,Lesson 30
Les parative and Superlative Adjectives son 12.4More ComSE/TWE pp. 457458 FOCUS Objectives:To identify irregular comparative and superlative negative comparative and superlative adjectives correctly; to forms properly in speaking and writing
Bellringer and Motivating Activity, TWE p. 457 TEACH Grammar Tip, TWE p. 457 TwoMinute Skill Drill, TWE p. 458 Critical Thinking, TWE p. 458 PRACTICE AND ASSESS Answers: Exercises 7 and 8, TWE p. 458 Additional Resources Bellringer Activities TransparenciesGrammar Practice,p. 21 Daily Language Practice TransparenciesGrammar Reteaching,p. 24 TwoMinute Skill Drill TransparenciesGrammar Enrichment,p. 21 Grammar Workbook,Lesson 31 CLOSE Close activity, TWE p. 458
Lesson Plan Teachers Name......................................................................................Date.......................................................................... Grade..................................Class(es)....................................................Date(s)...............................................M Tu W Th F
Lesson 12.5 DemonstrativesSE/TWE pp. 45946 FOCUS Objectives:To identify demonstratives and to determine pronouns; to use demonstratives correctly in sentences
Bellringer and Motivating Activity, TWE p. 459
TEACH Teaching Tip, TWE p. 459 Writing in the Real World, TWE p. 460
PRACTICE AND ASSESS Answers: Exercises 9 and 10, TWE p. 460
Additional Resources Bellringer Activities Transparencies Daily Language Practice Transparencies Grammar Practice,p. 22
CLOSE Close activity, TWE p. 460
Grammar Reteaching,p. 25 Grammar Enrichment,p. 22 Grammar Workbook,Lesson 32
Lesson 1AdverE pp. 461462 2.6bsSE/TW FOCUS Objectives:To identify adverbs and the words that they modify; to use adverbs correctly
Bellringer and Motivating Activity, TWE p. 461
TEACH Critical Thinking, TWE p. 461 Critical Thinking, TWE p. 462
PRACTICE AND ASSESS Answers: Exercises 11 and 12, TWE p. 462
Additional Resources Bellringer Activities Transparencies Daily Language Practice Transparencies Grammar Practice,p. 23
CLOSE Close activity, TWE p. 462
98Writers Choice:Lesson Plans,Grade
Grammar Reteaching,p. 26 Grammar Enrichment,p. 23 Grammar Workbook,Lesson 33
Lesson Plan Teachers Name......................................................................................Date.......................................................................... Grade..................................Class(es).....................................................Date(s)...............................................M Tu W Th F Lesson 12.7WE pp. 46346 IntensifiersSE/T FOCUS Objectives:To identify intensifiersadverbs that m intensifiers correctly
Bellringer and Motivating Activity, TWE p. 4
TEACH Grammar Tip, TWE p. 463 Exploring Language, TWE p. 464
PRACTICE AND ASSESS Answers: Exercises 13 and 14, TWE p. 464
Additional Resources Bellringer Activities Transparencies Daily Language Practice Transparencies Grammar Practice,p. 23
CLOSE Close activity, TWE p. 464
Grammar Reteaching,p. 26 Grammar Enrichment,p. 24 Grammar Workbook,Lesson 34
Lesson 12.8 Comparative and Superlative AdverbsSE/TWE pp. 465466 FOCUS Objectives:To identify comparative and superlative comparative and superlative adverbs correctly
Bellringer and Motivating Activity, TWE p. 4
TEACH Teaching Tip, TWE p. 465 Cooperative Learning, TWE p. 465 TwoMinute Skill Drill, TWE p. 466 Cultural Connections, TWE p. 466
PRACTICE AND ASSESS Answers: Exercise 15, TWE p. 466
Additional Resources Bellringer Activities Transparencies Daily Language Practice Transparencies
CLOSE Close activity, TWE p. 466
TwoMinute Skill Drill Transparencies Grammar Workbook,Lesson 35
Lesson Plan Teachers Name......................................................................................Date.......................................................................... Grade..................................Class(es)....................................................Date(s)...............................................M Tu W Th F 12.9 LessonUsing Adverbs and AdjectivesSE/FOCUS Objectives:To distinguish between adverbs that follow verbs and predicate adjectives to add detail and to clarify writing a
Bellringer and Motivating Activity, TWE p. 467
TEACH Teaching Tip, TWE p. 467 Exploring Language,TWE p. 468
PRACTICE AND ASSESS Answers: Exercises 16 and 17, TWE p. 468
Additional Resources Bellringer Activities Transparencies Daily Language Practice Transparencies Grammar Practice,p. 25
CLOSE Close activity, TWE p. 468
Lesson 12.10
Grammar Reteaching,p. 27 Grammar Enrichment,p. 25 Grammar Workbook,Lesson 36
Avoiding Double NegativesSE/ TWE pp. 469470
FOCUS Objectives:To identify negative words, including contracted correctly and to avoid double negatives in speaking and writi
Bellringer and Motivating Activity, TWE p. 469
TEACH Critical Thinking, TWE p. 469 LessProficient Readers, TWE p. 470 PRACTICE AND ASSESS Answers: Exercises 18 and 19, TWE p. 470 Additional Resources Bellringer Activities Transparencies Daily Language Practice Transparencies Grammar Practice,p. 26 CLOSE Close activity, TWE p. 470 100WriterLesson Plans,s Choice:Grade
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Lesson Plan Teachers Name......................................................................................Date.......................................................................... Grade..................................Class(es).....................................................Date(s)...............................................M Tu W Th F Unit 12mmar ReviewSE/TWE pp. 47147 Gra
TEACH About the Literature, TWE p. 471 Linking Grammar and Literature, TWE p. 471 Teaching Tip, TWE p. 471 Critical Thinking, TWE p. 471 Viewing the Art, TWE p. 475 PRACTICE AND ASSESS Answers: Exercises 18, TWE pp. 472476 Additional Resources Grammar Workbook, Lessons 2837;Unit 5 Review; Cumulative Review: Units 15 CLOSE Close activity, TWE p. 476 Writing Applicationp. 477 Adjectives in Writing, TWE p. 477 Techniques with Adjectives, TWE p. 477 Practice, TWE p. 477
Assessment Options Tests with Answer Key & Rubrics Unit 12 Mastery Test, pp. 4748 Testmaker Unit 12 Mastery Test MindJogger Videoquizzes Interactive Tutor: Self Assessment,Unit 12
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