mathematics

Jens Carsten Jantzen

Jens Carsten Jantzen is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Jens Carsten Jantzen rather than just read about it. In short: Jens Carsten Jantzen (born 1948) is a German mathematician and professor emeritus at Aarhus University working on representation theory and algebraic groups. He introduced the Jantzen filtration and translation functors.

Key takeaways

Jens Carsten Jantzen belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Jens Carsten Jantzen to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Jens Carsten Jantzen from memory before moving on to harder problems.

Reference excerpt

Jens Carsten Jantzen (born 1948) is a German mathematician and professor emeritus at Aarhus University working on representation theory and algebraic groups. He introduced the Jantzen filtration and translation functors.

Early life and education Jantzen was born in 1948 in Störtewerkerkoog, Nordfriesland. He received his PhD from the University of Bonn in 1973 under the supervision of Jacques Tits.

Career In the late 1970s, Jantzen and Gregg Zuckerman independently introduced translation functors. In 1979, he introduced the Jantzen filtration. His doctoral students include Wolfgang Soergel.

Awards and honors In 2012 he became a fellow of the American Mathematical Society.

Selected publications Jantzen, Jens Carsten (1979), Moduln mit einem höchsten Gewicht, Lecture Notes in Mathematics, vol. 750, Berlin, New York: Springer-Verlag, doi:10.1007/BFb0069521, ISBN 978-3-540-09558-3, MR 0552943 Jantzen, Jens Carsten (1983), Einhüllende Algebren halbeinfacher Lie-Algebren, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)] (in German), vol. 3, Berlin, New York: Springer-Verlag, ISBN 978-3-540-12178-7, MR 0721170 Jantzen, Jens Carsten (1996), Lectures on quantum groups, Graduate Studies in Mathematics, vol. 6, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0478-0, MR 1359532 Jantzen, Jens Carsten (2003) [1987], Representations of algebraic groups, Mathematical Surveys and Monographs, vol. 107 (2nd ed.), Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-3527-2, MR 2015057 Jantzen, Jens Carsten; Schwermer, Joachim (2006), Algebra, Springer-Lehrbuch, Springer-Verlag, doi:10.1007/3-540-29287-X, ISBN 978-3-540-21380-2 Borho, Walter; Jantzen, Jens Carsten (1977). "Über primitive Ideale in der Einhüllenden einer halbeinfachen Lie-Algebra". Inventiones Mathematicae. 39: 1–53. Bibcode:1977InMat..39....1B. doi:10.1007/bf01695950. S2CID 118474214.

References

External links Home page of Jens Carsten Jantzen Pictures from Oberwolfach

Illustrations

Worked examples

Example 1 — a first encounter with Jens Carsten Jantzen

Start with the simplest possible case. Write down what Jens Carsten Jantzen claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Jens Carsten Jantzen before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Jens Carsten Jantzen ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Jens Carsten Jantzen

In research: Jens Carsten Jantzen appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Jens Carsten Jantzen in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Jens Carsten Jantzen is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1948 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Jens Carsten Jantzen outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Jens Carsten Jantzen in 20 minutes

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Close the page and write down what Jens Carsten Jantzen means in your own words.
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Frequently asked questions

What is Jens Carsten Jantzen in simple terms?

Why does Jens Carsten Jantzen matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Jens Carsten Jantzen?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Jens Carsten Jantzen.